This is an archive of some of the abstracts of the Math department colloquium.

### Schedule for 2017–2018

**Rama Mishra**

Title: Some interesting spaces associated to polynomial knots

Date: May 8 (Tuesday), 2018

Time: 3:00–4:00pm

Room: MB 126

**Brian Harbourne**

Title: Rational amusements for a winter afternoon

Date: March 13 (Tuesday), 2018

Time: 3:00–4:00pm

Room: ILC 403

**Yuanzhe Xi**

Title: Fast and stable algorithms for large-scale computation

Date: February 21 (Wednesday), 2018

Time: 3:00–4:00pm

Room: ILC 201

**Jonah Reeger**

Title: Numerical quadrature over bounded smooth surfaces

Date: February 16 (Friday), 2018

Time: 3:00–4:00pm

Room: ILC 201

**Michal Kopera**

Title: Adaptive high-order continuous/discontinuous Galerkin model of the ocean with application to Greenland fjords

Date: February 13 (Tuesday), 2018

Time: 3:00–4:00pm

Room: ILC 403

**Varun Shankar**

Title: A high-order meshfree framework for solving PDEs on irregular domains and surfaces

Date: February 9 (Friday), 2018

Time: 3:00–4:00pm

Room: ILC 201

**Tomáš Tichý**

Title: Recent innovations in portfolio selection strategies

Date: November 9 (Thursday), 2017

Time: 3:00–4:00pm

Room: MB 124

**Aaron Bertram**

Title: Complex vs Tropical Algebraic Geometry

Date: October 12 (Thursday), 2017

Time: 3:00–4:00pm

Room: MB 124

**Bengt Fornberg**

Title: Numerical Solutions of the Painlevé Equations

Date: September 15 (Friday), 2017

Time: 1:30–2:30pm

Room: ILC 401

**Laurie Cavey**

Title: Supporting Prospective Secondary Mathematics Teacher Learning About Student Reasoning: Rationale, Goals, and Strategies

Date: September 14 (Thursday), 2017

Time: 1:00–2:00pm

Room: ILC 404

**Jonathan Woody**

Title: A Statistical Analysis of Daily Snow Depth Trends in North America

Date: September 8 (Friday), 2017

Time: 1:30–2:30pm

Room: ILC 201

### Schedule for 2016–2017

**Rama Mishra**

Title: Real Rational Knots

Date: May 9 (Tuesday), 2017

Time: 3:00–4:00pm

Room: MB 139

A Real rational knot of degree d is an embedding of RP^1 to RP^3 defined by $[t,s]\to[p_0(t,s), p_1(t,s), p_2(t,s), p_3(t,s)]$ where p_i(t,s) are homogeneous polynomials of same degree d, that do not vanish simultaneously. It is easy to see that all knots in RP3 are isotopic to some real rational knot. Real rational knots can be categorized in two groups: the one that lie completely in R^3 and the one that intersect a plane at infinity. we call the first one as affine knots and the other one as projective knots. Real rational affine knots are same as our classical knots. Real rational knots are projective closure of maps R to R^3 given by $t\to(r_0(t),r_1(t),r_2(t),r_3(t))$ where r_i(t) are rational functions. This talk will present a technique to construct a real rational knot of reasonably low degree which is ambient isotopic to a given affine knot. We will generalize it to obtain real rational knots isotopic to any projective knot.

**Klaus Volperts**

Title: On the Mathematics of Income Inequality

Date: April 20 (Thursday), 2017

Time: 3:00–4:00pm

Room: MB 135

Abstract: The Gini-Index based on Lorenz Curves of income distributions has long been used to measure income inequality in societies. This single-valued index has the advantage of allowing comparisons among countries, and within one country over time. However, being a summary measure, it does not distinguish between intersecting Lorenz curves, and may not detect certain sociological and economic trends over time. We will discuss a new two-parameter model for the Lorenz curve, essentially the product of two `Pareto` distributions. This allows us to split the Gini-Index in two: One for the upper end and one for the lower end of the income ladder. This in turn allows us to observe phenomena in American history that are obscured when just viewing the Gini-Index alone. The talk will be accessible to anyone with just basic knowledge of calculus.

**Joe Champion**

Title: Do We Really Need More Standards? Considering the New Standards for Preparing Teachers of Mathematics

Date: April 7 (Friday), 2017

Time: 4:00–5:00pm

Room: MB 107

Abstract: Somewhat surprisingly, the new Standards for Preparing Teachers of Mathematics (Association of Mathematics Teacher Educators, 2017) is the first publication to present a comprehensive vision for both (1) the knowledge, skills, and dispositions well-prepared beginning teachers should have and (2) how teacher education programs can ensure their students meet those standards. We will discuss how these new standards might inform courses, programs, and policy at Boise State University. Students, faculty, and stakeholders are all welcome to join the conversation.

**Nick Trefethen**

Title: Cubature, Approximation, and Isotropy in the Hypercube

Date: March 16 (Thursday), 2017

Time: 3:00–4:00pm

Room: ILC 402

**Lilian Calderón-Garcidueñas** (Joint colloquium with the School of Nursing)

Title: Air pollution and your brain: the bad, the ugly and the expected!

Date: March 2 (Thursday), 2017

Time: 3:00–3:50pm

Room: MB 135

**Bob Palais**

Title: Math and DNA-based Medicine

Date: October 27 (Thursday), 2016

Time: 3:00–3:50pm

Room: MB 124

**Jaechoul Lee**

Title: Trend Estimation for Climatological Extremes

Date: September 14 (Wednesday), 2016

Time: 3:00–3:50pm

Room: MB 126

**Liljana Babinkostova**

Title: On games, latin squares and anomalous numbers

Date: September 7 (Wednesday), 2016

Time: 3:00–3:50pm

Room: ILC 303

### Schedule for 2015–2016

**Samuel Coskey**

Title: The complexity of classification problems

Date: Wednesday, 27 April 2016

Time: 3:00–3:50pm

Room: MB 124

**Bruce Reznick**

Title: The secret lives of polynomial identities

Date: Thursday, 21 April 2016

Time: 1:30–2:20pm

Room: RFH 312

**Ellen Veomett**

Title: Coloring Geometrically Defined Graphs

Date: Thursday, 14 April 2016

Time: 4:00–4:50pm

Room: ILC 302

**Joe Champion**

Title: Factors Affecting High School Calculus Completion Rates

Date: Friday, 8 April 2016

Time: 3:00–3:50pm

Room: ILC 403

**Liang Peng**

Title: Statistical Inference for the Lee-Carter Mortality Model

Date: Friday, 18 March 2016

Time: 3:00–3:50pm

Room: MB 139

**Varun Shankar**

Title: Radial Basis Function Methods for Meshfree Transport on the Sphere and Other Surfaces

Date: Thursday, 10 March 2016

Time: 3:00–3:50pm

Room: RFH 102-B

**Partha Sarathi Mukherjee**

Title: Image denoising using local pixel clustering

Date: Thursday, 3 March 2016

Time: 3:00–3:50pm

Room: ILC 302

**Ludger Overbeck**

Title: Multivariate Markov Families of Copulas

Date: Thursday, 18 February 2016

Time: 3:00–3:50pm

Room: MB 139

**Hirotachi Abo**

Title: Jordan canonical forms: from a commutative algebra point of view

Date: Thursday, 11 February 2016

Time: 3:00–3:50pm

Room: ILC 302

**Alex Townsend**

Title: Continuous analogues of matrix factorizations

Date: Thursday, 4 February 2016

Time: 3:00–3:50pm

Room: ILC 302

**Donna Calhoun**

Title: Parallel, adaptive finite volume methods for mapped, multi-block domains

Date: Tuesday, 15 September 2015

Time: 3:00–3:50pm

Room: ILC 401

**Grady Wright**

Title: Numerically solving partial differential equations on surfaces using kernels

Date: Friday, 11 September 2015

Time: 12:00–12:50pm

Room: ILC 204

**Sasha Wang**

Title: Identifying Similar Polygons: Comparing Pre-service Teachers’ Geometric Discourse with a Mathematician’s

Date: Thursday, 10 September 2015

Time: 3:00–3:50pm

Room: ILC 401

### Schedule for 2014–2015

**Stefano De Marchi**

Title: Multivariate Christoffel functions and hyperinterpolation

Date: Thursday, 19 March 2015

Time: 3:00–3:50pm

Room: ILC 404

**Carsten Burstedde**

Title: Recent Developments in Forest-of-octrees AMR

Date: Thursday, 12 March 2015

Time: 3:00–3:50pm

Room: ILC 404

**Michael Dorff**

Title: Analytic functions, harmonic functions, and minimal surfaces

Date: Monday, 23 February 2015

Time: 3:00–3:50pm

Room: ILC 303

**Jarosław Buczyński**

Title: Constructions of k-regular maps using finite local schemes

Date: Thursday, 6 November 2014

Time: 3:00–3:50pm

Room: ILC 304

**Jennifer Halfpap Kacmarcik**

Title: What is a Singular Integral Operator

Date: Thursday, 30 October 2014

Time: 3:00–3:50pm

Room: ILC 304

**Gregory G. Smith**

Title: Nonnegative sections and sums of squares

Date: Thursday, 23 October 2014

Time: 3:00–3:50pm

Room: ILC 304

**Jennifer Halfpap Kacmarcik**

Title: Sums of Squares Problems in Several Complex Variables

Date: Thursday, 25 September 2014

Time: 3:00–3:50pm

Room: ILC 301

### Schedule for 2013–2014

**Martino Lupini**

Title: An invitation to sofic groups

Date: Tuesday, 22 April 2014

Time: 2:00–2:50pm

Room: ILC 204

**Dr. Rama Mishra**

Title: Some numerical knot invariants through polynomial knots

Date: Wednesday, 25 September 2013

Time: 12:00–12:50pm

Room: B 207

**Dr. M. Randall Holmes**

Title: The consistency problem for New Foundations

Date: Tuesday, 10 September 2013

Time: 3:00–3:50pm

Room: ILC 204

**Dr. Zach Teitler**

Title: Recent advances in Waring rank and apolarity

Date: Thursday, 5 September 2013

Time: 3:00–3:50pm

Room: ILC 303

### Schedule for 2012–2013

**Dr. Robert Floden**

Title: Improving the Preparation of STEM Teachers: Improving Both Content Preparation and Teaching Practice

Date: Wednesday, 8 May 2013

Time: 4:00–5:30pm

Room: Student Union Building: Bergquist Lounge

**Dr. Rodrigo Platte**

Title: Algorithms for recovering smooth functions from equispaced data and the impossibility theorem

Date: Thursday, 2 May 2013

Time: 12:00–12:50pm

Room: ILC 404

**Dr. Samiran Sinha**

Title: Conditional logistic regression analysis when a covariate is measured with errors

Date: Thursday, 14 March 2013

Time: 3:00–3:50pm

Room: ILC 302

**Dr. Derrick Stolee**

Title: Uniquely Kr-Saturated Graphs — Infinite Families Using Cayley Graphs

Date: Tuesday, 22 January 2013

Time: 3:00–3:50pm

Room: ILC 203

**Dr. Holly Swisher**

Title: Ramanujan type supercongruences

Date: Thursday, 13 December 2012

Time: 12:00–12:50pm

Room: ILC 304

**Dr. Alex Woo**

Title: Some local properties of Schubert varieties

Date: Thursday, 8 November 2012

Time: 1:30–2:20pm

Room: B101

**Dr. Colleen Robles**

Title: Schubert varieties as variations of Hodge structure

Date: Thursday, 4 October 2012

Time: 1:30–2:20pm

Room: MG 120

**Dr. Laurie Cavey**

Title: Understanding Mathematical Definitions: What we are Learning from Students and Mathematicians

Date: Friday, 14 September 2012

Time: 12:00–12:50pm

Room: MG 120

### Schedule for 2011–2012

**Frank Stenger**

Title: Approximating indefinite convolutions

Date: Friday, 4 May 2012

Time: 1:40–2:30pm

Room: ILC 402

**Hirotachi Abo**

Title: Counting the number of complete subgraphs in the Paley graph

Date: Thursday, 8 March 2012

Time: 1:40–2:30pm

Room: ILC 204

**Jacek Kierzenka**

Title: Developing BVP solvers for MATLAB

Date: Monday, 5 March 2012

Time: 2:40–3:30pm

Room: ILC 401

**Lawrence C. Washington**

Title: Manipulating Encrypted Data

Date: Thursday, 1 March 2012

Time: 1:40–2:30pm

Room: ILC 301

**Michael Starbird**

Title: Geometric Gems: Appreciating the Timeless Beauty of Mathematics

Date: Thursday, 15 September 2011

Time: 4:00–5:00pm

Room: SUB Lookout Room

**Andres Caicedo**

Title: Sets and Games

Date: Thursday, 1 September 2011

Time: 1:40–2:30pm

Room: MG 120

### Schedule for 2010–2011

**Christine Escher**

Title: Classifying families of manifolds

Date: Thursday, 14 April 2011

Time: 2:40–3:30pm

Room: ILC 302

**Thomas Foster**

Title: Church-Oswald Models for Set Theory

Date: Thursday, 7 April 2011

Time: 2:40–3:30pm

Room: MG 108

**Uwe Harlander**

Title: The differentially heated rotating annulus as a laboratory analogue of the atmospheric circulation

Date: Thursday, 17 March 2011

Time: 2:40–3:30pm

Room: MG 108

**Lyudmyla Barannyk**

Title: Spatially averaged dynamics, closure method and dimension reduction for discrete models of heterogeneous continua

Date: Monday, 7 February 2011

Time: 2:40–3:30pm

Room: MG 124

**Dik Dummar**

Title: Uncertainty Quantification of a chemical kinetic process internship at Idaho National Laboratory

Date: Thursday, 27 January 2011

Time: 4:40–5:30pm

Room: MG 120

**Michael Pernice**

Title: Modeling and Simulation at Idaho National Laboratory

Date: Thursday, 27 January 2011

Time: 3:40–4:30pm

Room: MG 120

**Jim Wolper**

Title: Computational Complexity of Quadrature Rules

Date: Thursday, 27 January 2011

Time: 2:40–3:30pm

Room: MG 124

**Timothy Barth**

Title: A Survey of Techniques for Uncertainty Propagation with Application to Computational Fluid Dynamics

Date: Wednesday, 17 November 2010

Time: 2:40–3:30pm

Room ILC 213

**J. Scott Carter**

Title: An Introduction to Quandles

Date: Thursday, 11 November 2010

Time: 2:40–3:30pm

Room MG 124

**Piotr Kokoszka**

Title: Two sample inference in functional linear models

Date: Thursday, 14 October 2010

Time: 2:40–3:30pm

Room MG 124

**Grady Wright**

Title: Geophysical Modeling on the Sphere with Radial Basis Functions

Date: Thursday, 09 September 2010

Time: 2:40–3:30pm

Room MG 124

**Liljana Babinkostova**

Title: Games and Dimension

Date: Thursday, 02 September 2010

Time: 2:40–3:30pm

Room MG 124

### Schedule for 2009–2010

**Diarmuid Crowley**

Title: The Mapping Class Groups of (n-1)-connected 2n-Manifolds” and “An Introduction to the Manifold Atlas Project: www.map.him.uni-bonn.de

Date: Tuesday, 11 May 2010

Time: 3:30–4:45pm

Room MG 118

**Gary Hagerty**

Title: Using Technology to Reach Out to the Individual Student Creating Success in Mathematics for All

Date: Monday, 12 April 2010

Time: 2:40–3:30pm

Room ILC 404

**Xinyu Sun**

Title: Several Games and Things we can learn from them

Date: Monday, 17 March 2010

Time: 2:40–3:30pm

Room ILC 201

**Scott MacLachlan**

Title: Fast Solvers for Geodynamic Flows

Date: Tuesday, 16 March 2010

Time: 2:00–3:00pm

Room tba

**Zach Teitler**

Title: Ranks of Polynomials

Date: Monday, 15 March 2010

Time: 2:40–3:30pm

Room MG 226

**Peter Scheiblechner**

Title: A Quick Tour through Algebra and Geometry

Date: Friday, 12 March 2010

Time: 2:40–3:30pm

Room MG 226

**Jens Harlander**

Title: Groups as Geometric Objects

Date: Friday, 11 September 2009

Time: 2:40–3:30pm

Room MG 120

**Tevian Dray and Corinne A. Manogue**

Title: Bridging the Gap between Mathematics and the Physical Sciences

Date: Friday, 4 September 2009

Time: 2:40–3:30pm

Room MG 120

### Schedule for 2008–2009

**Inanc Senocak**

Title: Rapid-Response Simulation of Forward and Inverse Problems in Atmospheric Transport and Dispersion

Date: Thursday, 19 March 2009

Time: 3:40–4:30pm

Room: MG 139

**Longin Jan Latecki**

Title: Multiscale Random Fields with Application to Contour Grouping

Date: Friday, 5 December 2008 (cancelled)

Time: 2:40–3:30pm

Room: MG 120

**Charles Livingston**

Title: A survey of knot invariants

Date: Friday, 21 November 2008

Time: 2:40–3:30pm

Room: MG 120

**Uwe Kaiser**

Title: Three-manifold Topology after Perelman

Date: Friday, 14 November 2008

Time: 2:40–3:30pm

Room: MG 120

**Rosemary A. Renaut**

Title: Statistical properties of the regularized least squares functional and a hybrid LSQR Newton method for finding the regularization parameter: application in image deblurring and signal restoration

Date: Wednesday, 29 October 2008

Time: 2:40–3:30pm

Room: MG 120

**Barbara Zubik-Kowal**

Title: Numerical solutions of thalamo-cortical systems

Date: Friday, 17 October 2008

Time: 2:40–3:30pm

Room: MG 120

**Mike Hitchman**

Title: Cosmic topology

Date: Friday, 10 October 2008

Time: 2:40–3:30pm

Room: MG 124

**Jeffrey Boerner**

Title: An introduction to knot invariants

Date: Friday, 3 October 2008

Time: 2:40–3:30pm

Room: MG 120

**Stefan Geschke**

Title: Extensions of Ramsey’s Theorem

Date: Friday, 26 September 2008

Time: 2:40–3:30pm

Room: MG 120

**Andres Caicedo**

Title: Intersecting families and definability

Date: Friday, 19 September 2008

Time: 2:40–3:30pm

Room: MG 120

**Kyungduk Ko**

Title: Wavelet-based Bayesian estimation of partially linear regression models with long memory errors

Date: Friday, 12 September 2008

Time: 2:40–3:30pm

Room: MG 124

**Jaechoul Lee**

Title: A Reformulation of Weighted Least Squares Estimators in Autocorrelated Regressions

Date: Friday, 5 September 2008

Time: 2:40–3:30pm

Room: MG 120

**Stephan Rosebrock**

Title: The Whitehead Conjecture-An Overview

Date: Friday, 29 August 2008

Time: 2:40–3:30pm

Room: MG 120

### Schedule for 2007–2008

**William A. Bogley**, Oregon State University

Title: The Stallings Proof on the Grusko-Neumann Theorem on Free Products of Groups

Date: Friday, 4 April 2008

Time: 3:40–4:30pm

Room: MG 108

**Edward J. Fuselier**, West Point

Title: Customized Approximation with Radial Basis Functions

Date: Thursday, 20 March 2008

Time: 3:50–4:40pm

Room: MG 139

**Bart Kastermans**, University of Wisconsin

Title: Maximal Cofinitary Groups

Date: Friday, 7 March 2008

Time: 2:40–3:30pm

Room: MG 107

**Jennifer Brown**, College of William and Mary

Title: Finding topologically interesting points in ß(X) under the continuum hypothesis

Date: Wednesday, 5 March 2008

Time: 3:40–4:30pm

Room: MG 107

**Dawn Teuscher**, University of Missouri

Title: Integrated versus single-subject paths in High School: what and how students learn

Date: Wednesday, 5 March 2008

Time: 1:40–2:30pm

Room: MG 113

**Grady Wright**, Boise State University

Title: A Colloquium in Commemoration of Prof. Gene Golub. Probability, linear algebra, and numerical analysis:the mathematics behind Google’s PageRank(TM) algorithm

Date: Friday, 29 February 2008

Time: 2:40–3:30pm

Room: MG 108

**Andres Caicedo**, Boise State University

Title: Forcing axioms and inner models

Date: Friday, 27 February 2008

Time: 3:40–4:30pm

Room: MG 139

**Gunter Fuchs**, University of Muenster

Title: Souslin Trees in Topology, Forcing and Algebra

Date: Friday, 25 February 2008

Time: 3:40–4:30pm

Room: MG 107

**Zdzislaw Jackiewicz**, Arizona State University

Title: Numerical Solution of Problems with Functional Dependence in Medicine and Biology

Date: Friday, 22 February 2008

Time: 3:40–4:30pm

Room: MG 106

**Jenny Salls**, University of Nevada

Title: Do Professional Development Practices Impact the Implementation of a Reform Mathematics Curriculum as Measured by Student Achievement?

Date: Tuesday, 5 February 2008

Time: 2:40–3:30pm

Room: MG 107

Abstract: Reform in the teaching of K-12 mathematics has resulted in the development of new curriculum materials emphasizing mathematical concepts and understandings as well as problem solving skills. Implementation of reform involves changing teacher beliefs as well as practices. Reformers suggest such changes require long-term, intensive professional development situated within the context of the school. Providing this professional development requires financial and human resources not typically available to schools. This study sought to identify whether typical professional development provided during textbook adoption does impact the implementation of a reform mathematics curricula as measured by student achievement.

Fourth and fifth grade teachers in the second year of implementing a reform curriculum were surveyed regarding their professional development experiences during the previous five years. Backward regression identified no teaching practices or professional development experiences that were related to gain in test scores. Additional analyses indicated differences between teachers in Title 1 and non-Title 1 schools, suggesting increased professional development or increased attention to academic standards may support implementation of a reform mathematics curriculum.

**Jessica Strowbridge**, Oregon State University

Title: Middle School Teachers’ Formative Use of a Feedback Guide

Date: Monday, 28 January 2008

Time: 3:40–4:30pm

Room: MG 107

Abstract: As part of a professional development program focused on mathematics problem solving, middle school teachers were introduced to a feedback guide intended to help them provide feedback to students and make instructional decisions. The teachers’ use of this feedback guide is the focus of this talk. I will discuss the extent to which teachers use the guide reliably, as well as the evidence of the teachers’ use of the feedback guide to inform follow-up instruction. Although the subjects of the study were middle school teachers, the discussion about instructional planning has implications for all levels of instruction.

**Robert D. Guy**, UC Davis

Title: Modeling Fibring Gel Formation: Continuous to Discrete

Date: Tuesday, 18 December 2007

Time: 2:00–3:00pm

Room: MG 115

**Rosemary A. Renaut**, Arizona State University

Title: Determining the Regularization Parameters for the Solution of Ill-posed Inverse Problems

Date: Friday, 30 November 2007

Time: 2:40–3:30pm

Room: MG 139

### Schedule for 2006–2007

**Rama Mishra**, Boise State University

Title: Polynomial Knot theory

Date: Friday, 27 April 2007

Time: 3:40pm

Room: MG 106

Abstract: Polynomials are the easiest functions to work with. If we have a space curve parametrized by polynomials which is an embedding of the real numbers in 3-space then its one point compactification will be a smooth embedding of the unit circle in the unit three sphere which is nothing but a knot in the classical sense. On the other hand it can esaily be seen that if we take an open knot K, then, up to equivalence, we can find a polynomial embedding from the real numbers to 3-space that can represent K. A knot represented by a polynomial embedding is referred to as a polynomial knot. Polynomial representations for equivalent knots are connected by a one parameter family of polynomial embeddings. Thus, there is a bijection between equivalence classes of knots and equivalence classes of polynomial knots. In this talk we show some estimates on the degree of the polynomials to represent a given knot type. We also discuss that polynomial knot theory may be employed to compute some known knot invariants.

**Nathan Geer**, Georgia Institute Of Technology

Title: Multivariable quantum invariants of links arising from Lie superalgebras

Date: Friday, 9 March 2007

Time: 3:40pm

Room: MG 139

Abstract: There are deep connections between quantum algebra and knot theory. Every representation of a semisimple Lie algebra gives rise to a quantum group invariant of knots. The Jones, Kauffman, and HOMFLY knot invariants are all examples of such invariants. Invariants arising from Lie algebras can be extended to Lie superalgebras. These new invariants are more powerful than invariants arising from Lie algebras and have interesting new properties. In this talk I will speak about multivariable invariants of links arising from finite dimensional modules of Lie superalgebra of classical type. In particular, I will start with a gentle introduction into knot theory. Then I will give the construction of the standard Reshetikhin-Turaev quantum group invariant of links and discuss how to modify this construction (in the case of Lie superalgebras) in order to define a non-trivial invariant of links. Finally, I will touch on how these invariants are related to other well known invariants including the multivariable Alexander polynomial and Kashaev’s quantum dilogarithm invariants of links. I plan on making this talk accessible to a general mathematical audience.

**Jens Harlander**, Western Kentucky University

Title: Cells, Collisions, Curvature: an Introduction to Combinatorial Topology

Date: Friday, 2 March 2007

Time: 3:40pm

Room: MG 139

In 1993 the Russian mathematician Anton Klyachko observed the following property which he described as “suitable for a school mathematics tournament”: Given a tesselated 2-sphere, i.e. a subdivision of the surface of the ball into regions, let a car drive around the boundary of each region in an anti-clockwise direction. The cars travel at arbitrary speed, never stop and visit each point on the boundary infinitely often. Then there must be at least two places on the sphere where complete crashes occur. He used this result to prove the Kervaire Conjecture for torsion-free groups (which had been open for 30 years). In my talk I will discuss Klyachko’s Car Crash Lemma and other properties of the 2-sphere and give applications to Combinatorial Topology and Group Theory.

**Alexander Felshtyn**, Boise State University

Title: Periodic orbits and Knots

Date: Friday, 23 February 2007

Time: 3:40pm

Room: MG 139

The lecture will discuss several interesting phenomena (topological, algebraic, analytic and arithmetic) which are observed in the study of periodic orbits of a dynamical system. The main topics are: 1. Poincare-Hopf theorem and Euler characteristic. 2. Lorenz knots.

3. Sharkovsky ordering. Period 3 implies Chaos. Julia sets. 4. Reidemeister torsion, dynamical zeta functions andcounting periodic orbits.

**Andreas Zastrow**, University of Gdansk

Title: Generalized covering spaces

Date: Monday, 29 January 2007

Time: 3:40pm

Room: MG 139

Abstract: This talk will be devoted to presenting a concept of generalizing the theory of covering spaces. I and Hanspeter Fischer (Ball State University, Muncie, Indiana) have been working about it in the past years. Classical covering space has proven to be a very useful concept for semilocally simply connected spaces. It allows to present a space as a quotient of a simply connected space and gives a natural presentation for its fundamental group. Our covering spaces are constructed with the idea, to rescue these properties for a wider class of spaces. Provided that the natural homomorphism from the fundamental group into the shape group is an embedding, we obtain a simply connected universal covering space X’ together with a natural projection from X’ to X such that the group of p-equivariant autohomeomorphisms will be naturally isomorphic to the fundamental group of X. However, p will have weaker properties than in the classical case, but it still will have the path- and homotopy-lifting property. Our work covers also other aspects, like a universal property, intermediate covering spaces, and the weakening of the criteria if the fundamental group is countable or if the base space is first countable. These results and the particular phenomena and difficulties of this covering construction will be illustrated at a number of examples. If time suffices the talk might compare our concept with some of the other (recent and less recent) attempts of generalizing covering spaces that I am aware of.

**Andres Caicedo**, California Institute of Technology

Title: Point set topology and determinacy

Date: Thursday, 16 November 2006

Time: 12:40pm

Room: MG 108

Abstract: Determinacy is the assertion that all infinite perfect information games on integers are determined. In these games, players I and II alternate playing integers, and an analysis of the sequences so obtained decides the winner. Such a game is determined if either player has a winning strategy, a way of choosing its integers that guarantees victory. Continuing work of A. Hogan, we study the structure of topological spaces under the assumption of determinacy, with an emphasis on metric spaces of the least well-ordered uncountable size.

**Razvan Gelca**, Texas Tech University

Title: On the physics of the Jones polynomial of a knot

Date: Friday, 3 November 2006

Time: 3:40pm

Room: MG 108

Abstract: The Jones polynomial is a knot invariant that is easy to compute but difficult to study. It has profound links to various areas of physics and geometry, among which: quantum field theory, statistical mechanics, and quantum groups. In the present talk we will discuss a surprising relation with the Weyl quantization procedure.

**Shawn Martin**, Sandia National Laboratories

Title: Molecular Design Using Chemical Fragments

Date: Thr. 19 October 2006

Time: 12:40pm

Room: MG 108

Abstract: I will describe a mathematical framework developed for the design of molecular structures with desired properties. This method uses fragments of molecular graphs to predict chemical properties. Linear Diophantine equations with inequality constraints are then used to re-organize the fragments into novel molecular structures. The method has been previously applied to problems in drug and materials design, including LFA-1/ICAM-1 inhibitory peptides, linear homopolymers, and hydrofluoroether foam blowing agents. I will provide a complete description of the method, including a new approach to overcome previous limitations due to combinatorial complexity. The new approach uses the Fincke-Pohst algorithm for lattice enumeration, implemented using the PARI/GP computer algebra library.

**Leming Qu**, Boise State University

Title: Determination of regularization parameter using L-curve by the LARS-LASSO algorithm

Date: Friday, 15 September 2006

Time: 3:40pm

Room: MG 115

Abstract: Regularization is a common technique to obtain reasonable solutions to ill-posed problems. In Tikhonov regularization, both the data-fitting and the penalty terms are in L2 norm. The L-curve is a plot of the size of the regularized solution versus the size of the corresponding residual for all valid regularization parameters. It is a useful tool for determining a suitable value of the regularization parameter in Tikhonov regularization. LASSO replaces the L2 norm by L1 norm for the penalty term. The LARS algorithm computes the whole path of the LASSO with a computational complexity in the same magnitude as the ordinary least squares. Thus, the L-curve for LASSO can be very efficiently obtained by the LARS-LASSO algorithm. The tuning point of the L-curve is chosen as the value of the regularization parameter. We compare L-curve method with the existing cross-validation method. The simulation suggests a better performance for the L-curve method.

### Schedule for 2005–2006

**Liljana Babinkostova**, Boise State University

Title: Selection principles and infinite games

Date: Monday, 1 May 2006

Time: 2:40pm

Room: MG 106

Abstract: Cantor’s diagonal argument is one of the classical tools of set theory. In classical literature several measure-like properties, basis properties or covering properties have been defined in terms of diagonalization processes. The area of selection principles unifies these studies by showing that each of these properties can be characterized by a typical diagonalization process, called a selection principle. Selection principles have natural infinite games associated with them. These games are powerful tools for developing the theory of these selection principles. In this talk we survey the selection principles S1(A,B), Sfin(A,B) and Sc(A,B) and their associated games. We show how they are related to basis properties, measure like properties, and also to Lebesgue’s covering dimension. We present some recent results in connection with the questions whether the Sierpinski basis property implies the Rothberger property, whether the product of a strictly o-bounded group and an o-bounded group is o-bounded and when finite powers of Haver spaces are Haver spaces.

**Scott MacLachlan**, University of Minnesota

Title: A Variational Approach to Upscaling Heterogeneous Media

Date: Monday, 24 April 2006

Time: 11:40am

Room: MG 121

Abstract: Sufficient resolution of fine-scale variations in material properties is often needed to achieve the high levels of accuracy demanded of computational simulation in biological and geophysical applications. In many cases, this variation is resolved on a scale that is finer than is practical to use for computation, requiring mathematical tools for coarsening (or upscaling) the medium or the model. The mathematical tools of homogenization address the question of determining effective properties of the medium on a coarser scale, but are, in general, not justified for media that arise in nature. In this talk, I discuss a new approach for upscaling PDE models with heterogeneous media based on variational principles. The variational framework used is based on that of Galerkin finite element discretizations and is closely related to that used in robust multilevel solvers, such as multigrid. As in robust geometric and algebraic multigrid methods, the coarsening procedure is induced by the fine-scale model itself. In this way, we construct a hierarchy of models that resolve the effects of the fine-scale structure at multiple scales. This research is in collaboration with J. David Moulton from Los Alamos National Laboratory.

**Gary Gruenhage**

Title: The double arrow space

(Canceled)

**Stanislav Jabuka**, University of Nevada

Title: Smooth 4-manifolds and Heegard Floer homology

Date: Friday, 14 April 2006

Time: 3:40pm

Room: MG 107

Abstract: This talk is a survey of important recent results from the theory of smooth 4-manifolds. Dimension 4 lives on threshold between low dimensions (1,2,3) and higher dimensions (5 and above) and as such exhibits phenomena not encountered in other dimensions. This makes the study of 4-manifolds particularly cumbersome and the main tools for manifold study – invariants of the smooth structure – have been very hard to construct. One such invariant, the Heegard Floer homology, has been discovered in 2001 by P. Ozsvath and Z. Szabo. It is the first example of a 3+1 dimensional TQFT and holds great potential to answer questions which have not been accessible via previously existing theories.

**Alexander Felshtyn**, Boise State University

Title: Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion

Date: Friday, 7 April 2006

Time: 3:40pm

Room: MG 107

Abstract: The study of dynamical zeta functions is part of the theory of dynamical systems, but is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. In the talk I will discuss the Reidemeister and Nielsen zeta functions. These zeta functions count periodic points of dynamical systems in the presence of fundamental group. Arithmetical congruences for Reidemeister numbers will be described. I will explain how dynamical zeta functions give rise to the Reidemeister torsion. This is an important topological invariant, which has useful applications in topology, quantum field theory and dynamical systems. The connection between symplectic Floer homology for surfaces and Nielsen fixed point theory will be described.

**Boaz Tsaban**, Weizmann Institute of Science

Title: A taste of infinite-combinatorial real analysis

Date: Tuesday, 21 March 2006

Time: 2:40pm

Room: MG 107

Abstract: Cantor’s diagonalization argument was invented and used to obtain a beautifully elegant proof of the existence of transcendental real numbers. Since then, the diagonalization method went a long way, and formed the field of set theory. There are still questions about the real line that are best treated using this approach. We give an overview of a subfield of set theory dealing with the real line from this point of view. The rapid development of this field in recent years owes much to the works of the mathematicians here at Boise. We will limit ourselves to a selected choice of topics, and introduce, step by step, all that is needed in order to open a window to this fascinating field of mathematics.

**Lin Wang**, University of Victoria

Title: Competition in the chemostat

Date: Tuesday, 28 February 2006

Time: 2:40pm

Room: MG 107

Abstract: In this talk, a chemostat model with general nonmonotone response functions is considered. The nutrient conversion process involves time delay. It is shown that under certain conditions, when several species with differential removal rates compete in the chemostat for a single resource that is allowed to be inhibitory at high concentrations, the competitive exclusion principle holds. In addition, a local stability analysis is provided that includes sufficient conditions for the bistability of the single species survival equilibrium and the washout equilibrium, thus showing initial condition dependent outcome is possible. Some related questions suitable for undergraduate students and graduate students will also be presented.

**Junling Ma**, McMaster University

Title: Why does influenza come back every winter?

Date: Tuesday, 21 February 2006

Time: 2:40pm

Room: MG 107

Abstract: A key characteristic of Influenza epidemics is that they occur in the winter. Traditionally, this seasonality is thought to arise from seasonal changes in transmission rates. However, fitting a seasonally forced transmission model to influenza mortality time series reveals that the periodic introduction of new flu variants may also play a fundamental role. In fact, we can fit the mortality curve very well with no seasonal variation in transmission rates. In this talk, we will see that flu-like cyclic dynamics can emerge from the coupling of the epidemic process (described by a deterministic compartmental model) and the viral mutation process (described by a nonhomogeneous Poisson process). While not required to generate periodicity, seasonal forcing ensures that the average period between epidemics is exactly one year. The results that I will describe suggest a variety of ways to develop tractable mathematical models that can further increase our understanding of influenza dynamics and evolution.

**Grady Wright**, University of Utah

Title: Recent developments in radial basis functions interpolation with applications to the geosciences

Date: Friday, 17 February 2006

Time: 2:40pm

Room: MG 106

Abstract: Radial basis functions (RBFs) are a powerful tool for interpolating/approximating scattered data. They easily generalize to multiple dimensions, handle arbitrarily scattered data, and can be spectrally accurate both for interpolation and for numerically solving partial differential equations (PDEs). Since their discovery in the early 1970s, both the knowledge about RBFs and their range of applications have grown tremendously. Some of these more recent applications include geophysics, neural networks, pattern recognition, and graphics and imaging. We will first review the basic properties of RBF interpolation and briefly discuss some recent computational algorithms for the resulting linear systems. We will then focus on two new RBF approaches for numerically solving PDEs. The first is a spectral collocation method for PDEs arising in climate modeling on the surface of a sphere. The second is on a local finite difference-type technique for PDEs on irregularly shaped domains.

**Jozef Przytycki**, George Washington University

Title: From Khovanov homology to Hochschild homology and back in 50 Minutes

Date: Friday, 4 November 2005

Time: 3:40pm

Room: MG 115

Abstract: We start this talk by describing the Tait construction of link diagrams from signed plane graphs, and conversely, the construction of signed plane graphs from link diagrams. In 1999 M. Khovanov introduced a homology theory which categorifies the Jones polynomial of links. We use the Tait construction to argue that one can understand Khovanov homology of links by describing first graph homology. Hochschild homology is the older theory, developed in 1945 to analyze rings and algebras. We show that Khovanov homology and Hochschild homology share common structure. In fact they overlap: Khovanov homology of a (2,n)-torus link can be interpreted as Hochschild homology of the algebra underlining the Khovanov homology. In the classical case of Khovanov homology we prove the concrete connection. In the general case of Khovanov-Rozansky, sl(n), homology and their deformations we conjecture the connection. The best framework to explore our ideas is to use a comultiplication free version of Khovanov homology for graphs developed by Y. Rong and L. Helme-Guizon. In this framework we prove that for any unital algebra A the Hochschild homology of A is isomorphic to graph homology over A of a polygon. We expect that this observation (that two theories meet) will encourage a flow of ideas in both directions betwewen Hochschild/cyclic and Khovanov homology theories.

**Peter Zvengrowski**, University of Calgary

Title: Riemann and his Zeta Function

Date: Friday, 7 October 2005

Time: 3:40pm

Room: MG 108

Abstract: This talk is intended as an elementary introduction to the Riemann zeta function and the related Riemann Hypothesis. Much of it will be from an historical perspective, e.g. we will attempt to ask and (possibly) answer questions such as ” how much did Riemann actually know about the RH?” and “did he consider it very important?” The developments since Riemann’s 1859 paper will also be discussed, as well as some recent research of the author.

**Fan Chung**, UC San Diego

Title: Random Graphs and Internet Graphs

Date: Monday, 19 September 2005

Time: 10:40am

Room: MEC 106

Abstract: Many very large graphs that arise in Internet and telecommunications applications share various properties with random graphs (while some differences remain). We will discuss some recent developments and mention a number of problems and results in random graphs and algorithmic design suggested by the study of these “massive” graphs.

**Ron Graham**, UC San Diego

Title: Searching for the Shortest Network

Date: Monday, 19 September 2005

Time: 3:40pm

Room: MP 106

Abstract: Suppose you are given some set of cities and you would like to connect them all together with a network with the shortest possible length. How hard is it to find such a short network? This classical problem has challenged mathematicians for nearly two centuries, and today has great relevance in such diverse areas as telecommunication networks, design of VLSI chips and molecular phylogenetics. In this talk we will summarize past accomplishments, present activities and future challenges in this fascinating topic.

### Schedule for 2004–2005

**Christina Hayes**, Montana State University

Title: A Generic Property of the Infinite Population Genetic Algorithm

Date: Monday, 2 May 2005

Time: 3:40pm

Room: MG 108

Abstract: Genetic Algorithms (GAs) are a class of stochastic search algorithms based on the idea of natural selection. I will give a brief introduction to GAs, as well as a dynamical systems model of GAs acting on an infinite population. We will then study an infinite population model for genetic algorithms, where the iteration of the algorithm corresponds to an iteration of a map G. The map G is a composition of a selection operator and a mixing operator, where the latter models effects of both mutation and crossover. We examine the hyperbolicity of fixed points of this model. We show that for a typical (generic) mixing operator all the fixed points are hyperbolic.

**Xiao-Song Lin**, UC Riverside

Title: An unfolding problem for polygonal arcs in the 3-space

Date: Friday, 29 April 2005

Time: 3:40pm

Room: MG 106

Abstract: Motivated by the protein folding problem in molecule biology, we will propose a mathematical problem about the unfolding of a certain kind of polygonal arcs in the 3-space. And we will discuss the possibility of extending the method developed in the recent solution of the classical carpenter’s ruler problem in the plane to this unfolding problem.

**Michael McLendon**, Washington College

Title: Studying 3-manifolds using knots

Date: Friday, 22 April 2005

Time: 3:40pm

Room: MG 108

Abstract: The skein module of a 3-manifold is an algebraic object formed by the types of knots and links that the manifold can contain. In the words of Jozef Przytycki, skein theory is “algebraic topology based on knots.” We will look at the skein module of a 3-manifold when the manifold is defined via a Heegaard splitting, M=H_0 U_F H_1. Here H_0 and H_1 are two solid handlebodies glued together to form M along their common boundary surface F. Using this Heegaard splitting of M in conjunction with the skein modules of H_0, H_1, and F, we can define an indexed list of modules called the Hochschild homology of the Heegaard splitting. The zeroth Hochschild homology recovers the information in the skein module of the manifold and the higher Hochschild homology modules may provide additional information about the manifold.

**Stefan Geschke**, Freie Universitat Berlin

Title: Convex Geometry, Continuous Colorings and Metamathematics

Date: Tuesday, 15 March 2005

Time: 2:40pm

Room: MG 118

I will give an overview over a number of results obtained by Kojman, Kubis, Schipperus and myself concerning certain cardinal invariants arising in convex geometry. For a subset S of a real vector space we consider the *convexity number* γ(S), the least cardinality of a family F of convex subsets of S which covers S. We are mainly interested in uncountable convexity numbers of closed subsets of R^n. In R^1 the situation is simple. For every closed subset S of R^1 either γ(S) is countable or there is a nonempty perfect subset P of S such that every convex subset of S intersects P in at most 2 points. In the latter case γ(S)=|R|. The situation is more complicated in R^2. For every closed subset S of R^2 exactly one of the following two statements holds: (1) There is a nonempty perfect subset P of S such that every convex subset of S intersects P in at most 3 points (and hence γ(S)=|R|). (2) There is a forcing extension of the set-theoretic universe in which γ(S)<|R| (and hence there is no set P as in (1)). The convexity numbers of closed sets satisfying (2) turn out to have a combinatorial characterization as so-called *homogeneity numbers* of continuous pair colorings on the Baire space $N^N$. The metamathematical issues involved in statement (2) will be discussed briefly. The dichotomy for closed subsets of R^2 cannot be generalized to higher dimensions. I will mention some results that are provable in higher dimensions.

**Bernhard Koenig**, Boise State University

Title: More than the sum of its parts

Date: Thursday, 10 March 2005

Time: 2:40pm

Room: MG 108

Abstract: We consider a couple of interesting phenomena in combinatorial set theory concerning trees (a tree is a partial ordering with the property that the predecessors of every point form a linear well- ordering). We ask the following question: assume we are given two trees S and T such that all proper initial segments of S are isomorphic to proper initial segments of T and vice versa (we call S and T “locally isomorphic” in this case). Does this mean that S and T are isomorphic? It seems paradoxical to have two trees S and T that are locally isomorphic but not isomorphic, since this would mean that they are constructed using the very same building blocks, yet they would be different. We present a couple of results (some are classical, some are more recent results of the speaker) that show that the question can have different answers, depending on the height of the trees and on the axioms of set theory.

**Andres Caicedo**, Kurt Goedel Research Center

Title: Stationary subsets of ω_{1} and models of set theory

Date: Tuesday, 22 February 2005

Time: 1:40pm

Room: MG 113

Abstract: A set X has size ω_{1} if it is uncountable, and every infinite subset of X has either the size of the natural numbers, or else it has the size of X, i.e., the version of the Continuum Hypothesis for X holds. Fixing such a set X, among its uncountable subsets a notion of ‘size’ can be introduced from which a rich combinatorial theory can be developed. A stationary subset of X is one that is ‘medium sized’ with respect to this notion. A model of set theory is a collection of sets that satisfies the axioms of set theory (in the same way that ‘a model of group theory’ is a collection M of objects that satisfies the axioms of group theory, i.e., M is a group). Given a model of set theory V and a submodel M, some element of M may be ‘stationary in M’ but not be ‘stationary in V’. We present two results that investigate these notions. The first says that there is always some preservation, i.e., certain stationary sets in M are stationary in V. The second studies restrictions in what M can be if an additional assumption (a so-called forcing axiom, related to preservation of stationary sets) is assumed of both M and V.

**Amir Togha**, George Washington University

Title: What initial segments do automorphisms fix?

Date: Thursday, 17 February 2005

Time: 2:00pm

Room: MG 108

Abstract: An automorphism of a model M is simply a permutation of M’s universe that preserves the structure of M. In this talk we discuss certain models of Arithmetic and Set Theory and their automorphisms. The notion of “initial segment” will be introduced for these models and the properties of the *largest* initial segments that are fixed by automorphisms will be investigated. The goal is to give a characterization of such initial segments for sufficiently rich models of Set Theory.

**Barbara Zubik-Kowal**, Boise State University

Title: How do elements of semi-discrete systems affect convergence of waveform relaxation?

Date: Thursday, 27 January 2005

Time: 1:40pm

Room: MG 108

Abstract: Waveform relaxation is an iterative method. It has an advantage that it can be applied in parallel computing environments. A further advantage is that implementation of implicit ODE solvers applied to the resulting waveform relaxation schemes is straightforward. No algebraic systems need to be solved in any time step, unlike the situation where waveform relaxation is not applied. These advantages are useful when solving both linear and nonlinear differential systems. We can replace nonlinear systems of ODEs by sequences of linear problems which can be effectively integrated by A(α)-stable backward differentiation methods or A-stable implicit Runge-Kutta methods. This allows for much larger time steps than those used for explicit methods. In this talk we present a new approach to the analysis of convergence of waveform relaxation. In our approach we investigate magnitutes of elements of differential systems. New results about relations between the elements and convergence of waveform relaxation are presented. Our theoretical results are new for both delay and non-delay linear and nonlinear differential equations. The results are confirmed by numerical experiments.

**Justin Moore**, Boise State University

Title: The L space problem, the oscillation function, and its applications

Date: Friday, 19 November 2004

Time: 3:40pm

Room: MG 106

Abstract: This talk will introduce the oscillation function and some of its applications in mathematics. A recent development in this area has been the use of this function to define a nonseparable topological space with no uncountable discrete subspaces (an L space), answering a problem asked by Hajnal and Juhasz in 1968. Examples of such spaces have long been known to be consistent with the usual axioms of mathematics (a Souslin Line is an L space), but this construction requires no additional axiomatic assumptions. The L space also has an interpretation as a coloring a bipartite graph. In particular, there is an edge coloring of an uncountable complete bipartite graph with infinitely many colors so that all colors appear on any uncountable bipartite subgraph (here uncountable bipartite means that both “camps” of vertices in the graph are uncountable). The oscillation function has also had application to the continuum problem. Forcing Axioms—certain strengthenings of Baire’s Category Theorem—often impose considerable restrictions on the cardinality of the real line and frequently imply that it is the second uncountable cardinal. Two of these proofs make crucial use of the oscillation function and its properties.

**Cynthia Hernon**, Northern Arizona University

Title: Teacher Exploration of Instructional Strategies to Promote Algebraic Thinking

Date: Monday, 15 November 2004

Time: 3:00pm

Room: MG 108

Abstract: The research study investigates the influence of teacher participation in a graduate course fostering the development of algebraic thinking for K-8 students on teacher understanding of the nature of algebraic thinking and on the incorporation of the teaching of algebraic thinking, guided by student discourse, into practice. This study explores how three elementary teachers introduce the algebraic concepts of equivalence, relational thinking, and the development and justification of conjectures to first and third grade students. The research is framed against the examination of teacher change in practice within the context of a professional development experience. The qualitative case study of these three elementary teachers is focused on the personal, situational, and institutional factors that are conducive to effecting this change in practice.

The constant comparative analysis of the data collected from interviews, classroom observations, journal reflections, and survey responses revealed six common themes across the cases. All three teachers possess a high level of interest in teaching mathematics, believe that traditional teaching strategies are not working for their students, demonstrate ambiguity about the definition of algebraic thinking, cite a lack of curriculum resources to support the teaching of algebraic thinking, desire collaboration with like-minded teachers, and are committed to continuing the teaching of algebraic thinking. These teachers successfully added to their mathematics content knowledge and either incorporated new pedagogy into their teaching or refined an existing constructivist approach to teaching and learning as they integrated the teaching of algebraic thinking into the classroom.

**Marta Asaeda**, University of Iowa

Title: Introduction to Khovanov homology and Recent Developments

Date: Monday, 18 October 2004

Time: 3:40pm

Room: MG 108

Abstract: I will give an introduction to Khovanov homology: a homology theory for links whose Euler characteristics are Jones polynomials. I further give an overview of recent developements.

**Matthias K. Gobbert**, University of Maryland – Baltimore County

Title: Numerical Simulations of Process Models in Microelectronics Manufacturing on Beowulf Clusters with High-Performance Networks

Date: Friday, 15 October 2004

Time: 3:40pm

Room: MG 139

Abstract: Production steps in the manufacturing of microelectronic devices involve gas flow at a wide range of pressures. We develop a kinetic transport and reaction model (KTRM) based on a system of time-dependent linear Boltzmann equations. A deterministic numerical solution for three-dimensional kinetic models requires the discretization of the three-dimensional velocity space, the three-dimensional position space, and time. We design a spectral Galerkin method to discretize the velocity space by specially chosen basis functions. For the spatial discretization, we use the discontinuous Galerkin finite element method. As an application example, we simulate chemical vapor deposition at the feature scale in two and three spatial dimensions and analyze the effect of pressure. Finally, we present parallel performance results which indicate that the implementation of the method possesses excellent scalability on a Beowulf cluster with a high-performance Myrinet network. I will describe the hardware of this system in some detail and discuss general issues involved in the assessment of performance in parallel computing.

### Schedule for 2003–2004

**Zbigniew Bartoszewski**, Gdansk University of Technology

Title: The existence and uniqueness of solutions and convergence of iterative methods for general differential-algebraic systems

Date: Friday, 7 May 2004

Time: 2:40pm

Room: MG 115

Abstract: The talk will be devoted to quite general classes of integro-algebraic and differential-algebraic systems. We do not require from the operators involved in the definitions of the systems under consideration to be of Voltera type. The existence and uniqueness of solutions to such systems as well as the convergence of different iterative processes of their solution including waveform relaxation methods will be discussed. There will be given constructive sufficient conditions under which the solutions exist and the iterative processes are convergent. A special attention will be paid to quasi-linear systems of differential-algebraic equations. A number of different iterative processes for their solution will be considered. The relationship between the spectral radii of the matrices that define the corresponding majorizing iterative processes will be provided. The talk will be concluded with numerical examples which illustrate how these spectral radii influence the rate of convergence of the iterative processes.

**Jodi L. Mead**, Boise State University

Title: Estimating Parameters in Mathematical Models

Date: Friday, 30 April 2004

Time: 2:40pm

Room: MG 115

Partial differential equations are used by scientists and engineers to model many different physical phenomenon. For example the wave equation (as its name suggests) can describe sound, light and water waves: d^{2}u/dt^{2}=c d^{2}u/dx^{2}, where c is the wave speed (wavelength/period) which depends on the type of wave being modeled and the medium through which the wave travels. In addition, u(x,t) is the measure of intensity of the wave at a particular location x and time t. Given the wave speed c, initial and boundary conditions, applied mathematicians are typically concerned with estimating u at some future point in time. On the other hand, geophysicists often send seismic or electromagnetic waves through the Earth’s subsurface, measure its intensity u and estimate the wave speed c. If they can accurately determine the wave speed, they have learned something about the composition of the Earth’s subsurface. Thus while applied mathematicians are typically concerned with solving the partial differential equation, scientists and engineers are in addition concerned with estimating the parameters in the model. I will discuss some traditional methods for estimating parameters m in the linear model d=Gm, and introduce an approach I am working on for estimating parameters and their uncertainty when the noise in the data is non-necessarily Gaussian.

**Kyungduk Ko**, Texas A&M University

Title: Bayesian wavelet approaches for parameter estimation and change point detection in long memory processes

Date: Thursday, 29 April 2004

Time: 2:40pm

Room: MG 108

Abstract: The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p; d; q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientic fields such as economics, finance, computer science and hydrology. Wavelets, being self-similar, have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p; d; q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p; d; q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform(DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the benchmark Nile river dataset.

**Margaret Kinzel**, Boise State University

Title: Does Studying Other Bases Help? Pre-service Elementary Teachers’ Strategies for Solving Place-Value Tasks

Date: Friday, 16 April 2004

Time: 2:40–3:30pm

Room: MG 115

Abstract: Bases other than ten have long been used in mathematics courses for elementary education majors, the rationale being that studying other bases leads to a deeper understanding of the familiar base-ten system. In spring 2001 the mathematics education research group conducted a small study to evaluate the effectiveness of studying other bases. We conducted interviews with 7 students selected from two sections of MATH 157. Within the interviews, the students were asked to talk about and solve problems in base ten as well as in other bases. In addition, students were asked to convert the `non-decimal’ 2.314 in base five to a base-ten numeral. This was a new representation for the students; it is not part of the content of MATH 157. We analyzed the students’ work and postulated two components necessary for a robust understanding of place value. The presentation will use interview data to illustrate the students’ strategies and articulate the components of understanding. Implications for instruction will be discussed.

**Matt Bognar**, University of Iowa

Title: Bayesian Inference for Pairwise Interacting Point Processes

Date: Friday, 2 April 2004

Time: 3:40–4:30pm

Room: MG 115

Abstract: In the past, inference in pairwise interacting point processes has been performed via frequentist methods. However, some frequentist methods can produce severely biased estimates when the data exhibit strong interaction. Furthermore, interval estimates are typically obtained by parametric bootstrap methods, but, in the current setting, the behavior of such estimates is unclear. We propose Bayesian methods for inference in pairwise interacting point processes. The requisite application of Markov chain Monte Carlo (MCMC) techniques is complicated by the existence of an intractable function of the parameters in the likelihood. The acceptance probability in a Metropolis-Hastings algorithm involves the ratio of two likelihoods evaluated at differing parameter values. The intractable functions do not cancel, and hence an intractable ratio must be estimated within each iteration of a Metropolis-Hastings sampler. Our unique implementation involves the use of importance sampling techniques within an MCMC sampler to estimate this intractable ratio. Although computationally costly, the ability to obtain interpretable posterior distributions justifies our Bayesian model-fitting strategy.

**Thomas Fiedler**, Universite Paul Sabatier Toulouse 3

Title: Knot theory for braids

Date: Thursday, 18 March 2004

Time: 2:40–3:30pm

Room: MG 108

Abstract: We give an overview about the conjugacy problem in braid groups. This problem was solved by Garside in 1969 in an algebraic manner. But the solution is of exponential complexity. It is conjectured by Thurston that there should be a solution of polynomial complexity. We will indicate such a solution which is obtained in a topological manner.

**Robert B. Lund**, University of Georgia

Title: Markov Chain and Renewal Rates of Convergence

Date: Monday, 8 March 2004

Time: 3:40–4:30pm

Room: MG 118

Abstract: We consider the problem of finding good geometric convergence rates for discrete-time renewal sequences and Markov chains. The goal is to identify an explicit rate bound and first constant that can be computed via minimal information. A general renewal convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to obtain renewal convergence rates for lifetimes possessing the new worse than used, new better than used, increasing hazard rate, decreasing hazard rate, and stochastically monotone structures. Attention is then directed to Markov chain convergence issues.

**Justin Moore**, Boise University University

Title: A five element basis for the uncountable linear orders

Date: Friday, 27 February 2004

Time: 2:40–3:30pm

Room: MG 115

Abstract: I will present a recent result in set theory: the class of uncountable linear orders consistently has a five elements basis. That is, there are five uncountable linear orders such that (consistently) any other uncountable linear order contains an isomorphic copy of one of these five. The list has long known to be minimal; it is provable from the usual axioms of mathematics that any basis must have at least five elements. It is not possible to prove such a result without appealing to additional axioms since, for instance, the Continuum Hypothesis implies that any basis must have as many elements as there are subsets of the reals. The talk will present each of the elements of the basis and discuss some of their properties. Some general remarks will also be made on the method of proof which can be considered as an infinitary version of Erdos’s probabilistic method.

**Zdzislaw Jackiewicz**, Arizona State University

Title: Construction and Implementation of General Linear Methods for Ordinary Differential Equations

Date: Friday, 20 February 2004

Time: 3:40–4:30pm

Room: MG 106

Abstract: In the first part of this lecture we will give the overview of different approaches to the construction of diagonally implicit multistage integration methods for both nonstiff and stiff differential systems of ordinary differential equations. The identification of high order methods with appropriate stability properties requires the solution of large systems of nonlinear equations for the coefficients of the methods. For low orders these systems can be generated and solved by symbolic manipulation packages. For high orders the approach to the construction of such methods is based on the computation of the coefficients of the stability function by a variant of the Fourier series method and then solving the resulting large systems of polynomial equations of high degree by least squares minimization. Using these approaches both explicit and implicit methods were constructed up to the order eight with good stability properties (Runge-Kutta stability for explicit methods, A-stability and L-stability for implicit methods). In the second part of this talk we will address different issues related to the implementation of general linear methods. They include selection of initial stepsize and starting values, computation of Nordsieck representation, efficient and reliable estimation of the local discretization errors for nonstiff and stiff equations, step size ond order changing strategies, construction of continuous interpolants, and updating vector of external approximations to the solution. Experiments with variable step variable order experimental Matlab codes for both nonstiff and stiff differential systems on interesting test problems will be presented and compared with appropriate codes from Matlab ODE suite. These experiments demonstrate the high potential of diagonally implicit multistage integration methods, especially for stiff systems of differential equations.

**Karen L. Ricciardi**, Bard College

Title: Developing a groundwater remediation system subject to uncertainty

Date: Friday, 16 January 2004

Time: 2:40–3:30pm

Room: MG 118

Abstract: A cost-effective groundwater pump-and-treat remediation design algorithm has been developed that takes into account the uncertainty of the hydraulic conductivity of a given aquifer. The resultant design is subject to both gradient constraints, which are linear with respect to changes in pumping rates, as well as concentration constraints, which are nonlinear with respect to changes in pumping rates. The uncertainty in the hydraulic conductivity is taken in to account in this model by using a multi-scenario approach whereby different hydraulic-conductivity fields, obtained through a representative sampling technique, are analyzed simultaneously. The tunneling method is a novel method of solving global-optimization problems of this form. This method has been modified to efficiently solve this optimization problem. An application to a hypothetical problem demonstrates the efficacy of this approach.

**Xiao-Wen Chang**, McGill University

Title: Numerical computations for GPS based position estimation

Date: Thursday, 11 December 2003

Time: 3:40–4:30pm

Room: MG 108

Abstract: It is now possible to find where you are. The measurements of position come from GPS (the Global Positioning System). GPS is a satellite based navigation system, which transmits signals that allow one to determine the location of GPS receivers. In this talk, it will be shown how numerical linear algebra techniques can be applied to this interesting area. I will use relative positioning (two receivers are used) as an example to show how to use the structures of the mathematical model to design an efficient and numerically reliable least squares algorithm for computing the position estimates. Real data test results will be presented to demonstrate the performance of our algorithm. This is a joint work with Professor Chris Paige.

**Uwe Kaiser**, Boise State University

Title: What is going on with the Poincare conjecture?

Date: Wednesday, 3 December 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: About a year ago the Russian mathematician Grigori Perelman announced a proof of the Geometrization Conjecture. This is concerned with the existence of certain geometric structures on 3-dimensional manifolds. It is known that the Geometrization Conjecture implies the famous Poincare Conjecture, a central problem in topology, open since 1904, and one of the seven Clay Problems. In this talk I will explain the mathematical contents of the Geometrization and Poincare Conjecture, and some ideas of Perelman’s approach.

**Nikos Apostolakis**, Boise State University

Title: Coloring Knots

Date: Wednesday, 19 November 2003

Time: 2:40–3:30pm

Room: MG 120

Abstract: Colorings of knots correspond to representations of the group of the knot into some symmetric group. We will examine such colorings both as a method of distinguishing knots and as representations of 3-dimensional manifolds. All terms will be explained during the talk.

**Karel in ‘t Hout**, Boise State University

Title: Direct methods for estimating Greeks with Monte Carlo

Date: Wednesday, 15 October 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: After a brief introduction into the pricing of options, using Monte Carlo simulation and stochastic differential equations, the talk would focus on estimating the sensitivities, the so-called Greeks, of option prices with respect to parameters that occur in the differential equation such as the interest rates and the volatility. These quantities play an important role in applications.

### Schedule for 2002–2003

**Vladimir Chernov**, Dartmouth College

Title: Affine Linking Numbers and the Causality Relation for Wave Fronts

Date: Tuesday, 13 May 2003

Time: 3:40–4:30pm

Room: MG 120

Abstract: The linking number is the classical invariant of the pair knots which is the number of intersections of one knot with a surface bounded by the other. We construct affine linking numbers that are extensions of linking numbers to the case where knots in question do not bound any surface. A CR causality invariant of the pair of fronts of two events is the algebraic number of times the earlier front has passed through the origin of the later front before the later front appeared, and it measures how strongly the earlier front influenced the event that caused the second front. We show that affine linking numbers can be effectively used to calculate the CR causality relation invariant from the current picture of the fronts of two signals without any knowledge of the signal propagation law. We also use it to count the algebraic number of times a front passed though a marked point between the two time moments.

**Liljana Babinkostova**, Boise State University

Title: Topological analysis of binary images and its applications in pattern recognition

Date: Friday, 25 April 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: Pattern recognition is the study of methods and the design of systems to recognize patterns in data. This area has applications in many fields, including image analysis, character recognition, speech analysis, identification, etc. In this talk we emphasize pattern recognition as classification: deciding if a given input belongs to a given category. Applying topology to analyzing images started in the 1970’s. Terms such as connectivity, boundary, interior, etc. are often encountered in this application. We use the notion of combinatorial homotopy equivalence to classify binary images into different categories, using such concepts as 0-Betti number, 1-Betti number and Euler characteristic.

**Jaechoul Lee**, University of Georgia

Title: Trends in United States Temperature Extremes

Date: Wednesday, 16 April 2003

Time: 2:40–3:30pm

Room: MG 120

Abstract: In this study, we investigate any linear trend inherent in monthly temperature minimums recorded at Lewiston, ME during the period 1887–2000. A statistical model is developed to quantify any temperature changes. Ordinary least squares estimates are computed with their standard errors under modeling of periodic features and site changes in the temperatures. An extreme value modeling based on generalized extreme value distributions is suggested. Maximum likelihood estimates are obtained and compared to the ordinary least squares estimates. Future analysis plan is listed for complete description of the trends in United States temperature extremes.

**Stefan Pittner**, Northeastern University

Title: Correlation and Predictability: Applications in Manufacturing

Date: Friday, 11 April 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: The problem of predicting a dependent numerical variable from an independent variable (or several independent variables) is generally approached with methods from approximation theory. In this talk it is demonstrated that establishing the predictability of a numerical variable is, however, mainly a problem of statistics. The importance of the predictability problem is demonstrated with an application in manufacturing process control. It is shown how existing concepts in statistics, such as statistical dependence, the Pearson correlation coefficient and the Spearman rank correlation coefficient, can be used for the evaluation of the predictability of a numerical variable. The merits and drawbacks of the concepts are discussed. Next, a nonparametric correlation measure called g-correlation coefficient is derived. The idea behind g-correlation is to replace the function approximation concept of predictability by a classification concept. The g-correlation concept allows one to detect (a) any monotonic relationship between the dependent and the independent variable and (b) a classification procedure in situations where accurate predictions are not possible. A method is proposed to estimate g-correlation from a set of samples for the variables under consideration. It is also sketched how g-correlation can be extended to more than one independent variable using Fisher linear discriminant functions. Results of the application of different correlation coefficients in a manufacturing application show that g-correlation has a central role among all standard concepts of correlation.

**Lisa Madsen**, Cornell

Title: Regression With Spatially Misaligned Covariates

Date: Tuesday, 18 March 2003

Time: 2:40–3:30pm

Room: MG 115

Abstract: When a response Y and a covariate X are measured in different spatial locations, we say the data are misaligned. This may occur when one of the variables is more difficult to measure, or when X and Y are measured by different agencies. Suppose we are interested in assessing the relationship of Y and X by estimating the parameters of a linear regression of Y on X, with X and Y misaligned. When X is generated by a spatially autocorrelated process, we can use the observed X’s to predict (krige) the covariate at the locations Y was observed. The predicted X’s can then be used in a standard regression analysis. This naive approach has an attractive simplicity. We will explore this method, obtaining expressions for the mean and variance of the estimator of the slope parameter, and assessing the performance of this estimator. We will show that it may be used with caution, and when the regression model has no intercept and E(X) is large, it performs nearly as well as if the data were not misaligned.

**Dan Canada**, Portland State University

Title: A Taste of Variation

Date: Friday, 14 March 2003

Time: 1:40–2:30pm

Room: MG 107

Abstract: Variation is a concept central to the twin domains of probability and statistics, yet research focusing on how children and their teachers understand variation has only been recently emerging. After discussing some earlier research and theoretical underpinnings, the methodologies of two current studies about conceptions of variation will be presented: An NSF-sponsored project focuses on the conceptions held by middle and high school students and their teachers, while ongoing doctoral research concerns the conceptions held by elementary preservice teachers. Sample tasks and responses will be shared to illustrate five key aspects comprising a conceptual framework for studying conceptions of variation.

**Kate Riley**, Montana State University

Title: An Investigation of Prospective Secondary Mathematics Teacher’s Conceptions of Proof and Refutations

Date: Friday, 7 March 2003

Time: 1:40–2:30pm

Room: MG 107

Abstract: A quantitative, descriptive research study was conducted to investigate prospective secondary mathematics teachers’ conceptions of proof and refutations as they were near completion of their preparation program. To research the primary question of the study, the researcher addressed two components of participants’ conceptions of proof: 1) understanding of the logical underpinnings of proof, and 2) ability to complete mathematical proofs. Both components focused on direct proof, indirect proof, and refutations. These components are common proof themes emphasized by the MAA (1998) and the NCTM Standards 2000.

**Craig Johns**, University of Colorado – Denver

Title: Infilling Sparse Records of Spatial Fields

Date: Monday, 3 March 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: Historical records of weather such as monthly precipitation and temperatures from the last century are an invaluable database to study changes and variability in climate. These data also provide the starting point for understanding and modeling the relationship among climate, ecological processes and human activities. However, these data are irregularly observed over space and time. The basic statistical problem is to create a complete data record that is consistent with the observed data and is useful to other scientific disciplines. We modify the Gaussian-Inverted Wishart spatial field model to accommodate irregular data patterns and to facilitate computations. Novel features of our implementation include the use of cross-validation to determine the relative prior weight given to the regression and geostatistical components and the use of a space filling subset to reduce the computations for some parameters. We feel the overall approach has merit, treading a line along computational feasibility and statistical validity. Furthermore, we are able to produce reliable measures of uncertainty for the estimates.

**Pete Caithamer**, West Point

Title: Stochastic Differential Equations and their Applications

Date: Thursday, 27 February 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: This talk will discuss the distributional properties of multiple stochastic integrals and their symmetrizations. Stochastic partial differential equations with both additive and multiplicative noises will then be considered. Particular attention will then be paid to the energy of the associated system and to the properties of the solution of that system. Extensions of results from the case of Brownian motion to the case of fractional Brownian motion will then be discussed. Finally an application of stochastic differential equations to radiative may be considered.

**Paul Larson**, Fields Institute

Title: Set Theory, Independence and Absoluteness

Date: Wednesday, 12 February 2003

Time: 2:40–3:30pm

Room: MG 121

Abstract: A sentence is independent of a set of axioms if there is no proof from the axioms of the sentence or its negation. Our primary means for demonstrating independence, forcing, was invented by Paul Cohen in the early 1960’s, and has been used since then to show that independence is widespread in set theory. Results in the other direction, limiting the independence phenomenon, are called absoluteness results. I will briefly sketch the history of these two lines of research, leading up to my own contributions. No previous knowledge of set theory or logic will be assumed.

**Justin Moore**, Boise State University

Title: Cantor’s Continuum Problem

Date: Wednesday, 11 Dec 2002

Time: 3:40–4:30pm

Room: MG 118

Abstract: In the early stages of the study of sizes of infinite sets, Cantor showed that the set of reals was uncountable. Thus he showed that there are two infinite sets of real numbers which have a different “sizes”—the set of all natural numbers and the set of all the real numbers. He asked whether it was possible to find a third set which, from the point of view of cardinality, lay strictly between these two sizes. It is now known that this problem cannot be decided within the framework of the usual axioms of mathematics. The purpose of this talk is to give an introduction to Cantor’s Continuum Problem, its resolution and the modern research which relates to it. First I will present a probabilistic interpretation of Cohen’s method of forcing and how he used it to solve the Continuum Problem. Next I will discuss Solovay’s results on the properties (including cardinality) of definable sets of reals and contrast this with Cohen’s work. Finally (time permitting) I will mention some of the work aimed at gaining a better understanding of the relationship between the size of the set of all reals and infinitary combinatorics (such as the study of uncountable graphs).

**Uwe Kaiser**, Boise State University

Title: String and skein topology of oriented 3-manifolds

Date: Wednesday, 13 November 2002

Time: 3:40–4:30pm

Room: MG 118

Abstract: The skein (or quantum) topology of links in oriented 3-dimensional manifolds has been studied intensely during the last 15 years. But the precise relation of the “new” invariants with the classical geometric topology of 3-manifolds is still not fully understood. Recently Moira Chas and Dennis Sullivan discovered new interesting algebraic structures on the (equivariant) homology groups of the space of maps from a circle into the 3-manifold. These structures are defined from “string interactions” in the manifold and are motivated by the string theory in physics ( a theory trying to unify quantum mechanics and general relativity theory). In the talk I will describe results concerning the relation between the string topology of Chas-Sullivan and the skein topology of oriented 3-manifolds.

**Will Alexander**, Capital One

Title: Analytics and Careers in the Financial Services Industry

Date: Wednesday, 23 October 2002

Time: 3:40–4:30pm

Room: MG 118

Abstract: The financial services industry is huge and tremendously varied. It spans the gulf from consumer finance to Wall Street, straight-forward amortizing loans to complex derivatives, billion dollar companies to mom-and-pop collection agencies. Throughout it all, analytics is the common currency. This talk addresses the types of work that is conducted, who’s doing it, their qualifications and potential career paths.

Bio: Dr. Alexander has been Director of Valuations at Capital One since March, 2002. Prior to Capital One, he was with First Union (1998-2002) in the Capital Markets and Risk Management groups and General Electric (1991-1998) at the Corporate R-D Center and NBC. He received his doctorate in statistics from Texas A and M (1989).

**M. Randall Holmes**, Boise State University

Title: Automated Reasoning in Predicate Logic and Set Theory using a Sequent Calculus

Date: Wednesday, 11 Sept 2002

Time: 3:40–4:30pm

Room: MG 118

Abstract: A formal system for reasoning in propositional logic, predicate logic and set theory will be described, and a computer implementation of reasoning in this system will be described and demonstrated. The formal system is a sequent calculus adapted from a system appropriated from a paper of Marcel Crabbe, which incorporates a safe version of Quine’s set theory New Foundations. One will not need to understand this description to understand what is going on in the talk. The computer program is an interactive proof checker rather than an automatic theorem prover: the user needs to construct the proofs of theorems (although automation in the program helps with organization of proofs); the role of the prover is to check the validity of the proof steps proposed by the user and display what remains to be proved after each step.

### Schedule for 2001–2002

**Justin Moore**, Boise State University

Title: The Method of Minimal Walks

Date: Tuesday, 30 April 2002

Time: 2:40 pm

Room: MG 118

Abstract: This talk will give an introduction to the first uncountable cardinal and some of the combinatorics and set theory associated with it. The method of minimal walks was developed by Todorcevic both to solve specific problems and to give a unified method for analyzing the first uncountable cardinal. The aim of the talk will be to give a “light” introduction to this method and mention some of the ways in which it can be used.

**Robert Sulanke**, Boise State University

Title: Moments and the Cut and Paste for Lattice

Date: Wednesday, 10 April 2002

Time: 3:30pm

Room: MG 106

Abstract: Abstract. Let U(2n) denote the set of lattice paths that run from (0,0) to (2n,0) with the permitted steps (1,1) and (1,-1). Let E(2n+2) denote the set of paths in U(2n+2) that run strictly above the horizontal axis except initially and finally. Starting with Wallis’ well-known formula for computing pi as an infinite product, we first establish an interest in lattice path configurations and their moments. We then introduce the cut and paste bijection which relates points under paths of E(2n+2) to points on paths of U(2n). We apply this bijection to obtain enumerations, some involving the Narayana distribution. We also extend the bijection to a formula relating factorial moments for the paths of E(2n+2) to moments for the paths of U(2n).

**Jodi Mead**, Boise State University

Title: Modeling Floats and Pollutants in the Ocean

Date: Wednesday, 5 December 2001

Time: 3:40pm

Room: MG 118

abstract: A good physical understanding of the ocean is necessary to (1) produce accurate short term weather forecasts, (2) give long term climate predictions, and (3) understand the effect of pollutants in the water. Deterministic partial differential equations, such as the Navier-Stokes equations, describe the dynamic process between pressure, temperature and velocity in the ocean. Data collected from the ocean can supplement these solutions. There are two basic ways to collect data from the ocean. One is to place moorings attached to the ocean floor. A second and less costly way, is to place floats in the ocean, let them drift, and collect their data by satellite. My work in oceanography involves solving a variant of the Navier-Stokes equation (the shallow water equations) from the viewpoint of floats, or pollutants in the water. This is a novel approach because most researchers find solutions at a fixed point in space (similar to what a mooring does). I will show some results from this model, and outline future work.

**Paul Corazza**, Boise State University

Title: Has Modern Mathematics Finally Understood The Infinite? The Good News And The Bad News

Date: Wednesday, 7 November 2001

Time: 3:40 pm

Room: MG 118

Abstract: Prior to the beginning of the 20th century, there was an almost superstitious fear among mathematicians of the concept of the infinite. It was believed, for example that, although the natural numbers “go on forever”, they cannot all be collected together into a single set. Such concerns were tied both to philosophical beliefs about the infinite and to paradoxes that were popular at the time. The work of Georg Cantor showed that unless infinite sets were allowed in mathematics, it would not be possible to have a completely rigorous calculus — even the concept of a “real number” depends on the concept of an infinite set. Nearly single-handedly, Cantor developed the foundation for the modern theory of infinite sets, which eventually became today’s axiomatic set theory, usually denoted ZFC. ZFC was seen by its creators to be a kind of ultimate foundation for all of mathematics: ZFC not only provided a framework for Cantor’s theory of infinite sets; it also provided a set of axioms from which all known theorems of mathematics could be derived. Ironically, even as ZFC was being developed, research in other areas of mathematics was uncovering certain bizarre mathematical entities–now known as large cardinals–which would eventually be shown to lie outside the framework of ZFC. In this talk, I’ll describe what a large cardinal is, and why they are important in mathematics. I’ll then describe an axiomatic framework that can provide the same kind of unifying foundation for “set theory + large cardinals” that ZFC has provided for the rest of mathematics.

**Justin Moore**, Boise State University

Title: Comparing braids, winning games, and other uses for really big numbers

Date: Wednesday, 24 October 2001

Time: 3:40 pm

Room: MG 118

Abstract: This talk will present some uses of infinity (of various sizes) in proofs of statements which do not, a priori, involve the infinite. In particular I will mention The Finite Kruskal Theorem (from graph theory), Goodstein’s Theorem (number theory/logic), Duhornoy’s braid comparison algorithm (knot theory), and Martin’s theorems concerning the determinacy of certain games (analysis/descriptive set theory).

**Scott Stevens**, University of Montana – Missoula

Title: Cardiac Forcing in Models of Human Hemodynamics

Date: Friday, 12 October 2001

Time: 1:40pm

Room: MG 120

Abstract: Many mathematical models of human circulatory dynamics require a preliminary function which accurately describes cardiac output. Approximations of human cardiac output are often given in terms of mean output, such as 5,000 mL/min. However, this description is of little use in resolving the pressure pulses caused by oscillations about the mean value. This talk develops and presents a “smooth”, periodic function describing ventricular output which accurately depicts these oscillations. The function is based on the heart rate and stroke volume as well as some preliminary assumptions regarding cardiac systole. The simplicity combined with the flexibility of this function makes it a practical forcing term for models of the human circulatory system describing normal and patho-physiology. In particular, this function is set in the context of a model describing human circulatory dynamics in microgravity. A good deal of this talk will be devoted to exploring the many aspects of this model.

**John Doherty**, Watermark Numerical Computing, Brisbane, Australia

Title: Environmental Modeling: Unveiling the Truth beneath the Fantasy

Date: Thursday, 4 October 2001

Time: 3:40pm

Room: MPC 201

Abstract: Alongside the growing use of models in environmental management, is a growing skepticism of the usefulness of these models. While many outside the modeling profession still cling to the idea that “if it comes from a computer it must be right”, there are a growing number of cases where the use of models in environmental management has been disappointing at best, and misleading at worst. In fact, there are signs of a crisis within the modeling profession. On the one hand there is general recognition that an attempt to simulate environment processes numerically can provide a sounder basis for the making of important decisions. On the other hand, many modelers are loathe to raise the expectations of their clients, or stakeholder groups, too high with regard to the usefulness of their models in the management process. So in this time of re-assessment, just how high should expectations be raised? And where exactly should modeling fit into the environmental management process? And should a modeler suffer a severe identity crisis if his/her model cannot provide the impossible “answer at the back of the book” that many are seeking from it?

The talk will attempt to address these questions by first demonstrating that predictions made by an environmental model will, by their very nature, be accompanied by a (sometimes frighteningly large) margin of uncertainty. It is demonstrated that the higher the level of “system detail” that a model attempts to simulate (eg, contaminant movement in areas of high geological heterogeneity, the response of a catchment to extreme climatic events, nuances of groundwater-surface water interaction, etc), the greater will be the uncertainty with which such predictions are made. Methodologies whereby model predictive uncertainty can be quantified will be discussed. Finally, a rationale will be presented for determining the “point of diminishing return” in the model construction process – this being the point where the data at hand, and our understanding of environmental processes on a field scale, precludes the devoting of any further resources to the building of a model.

**Margaret Kinzel**, Boise State University

Title: Analyzing College Calculus Students’ Interpretation and Use of Algebraic Notation

Date: Wednesday, 3 Oct 2001

Time: 3:40 pm

Room: MG 118

Abstract: My dissertation study investigated students’ interpretation and use of algebraic notation through task-based interviews. Ten calculus students participated in a sequence of four interviews in which they worked on nonroutine algebraic tasks. The analysis of the interviews focused on the ways in which students used and interpreted algebraic notation within the contexts of the tasks. Trends across an individual’s work as well as trends across participants were identified. In general, it was found that the participants, while comfortable with notation, lacked sufficient insight into algebraic notation to take full advantage of its potential. That is, the participants seemed able to apply a notational approach to familiar or routine tasks but lacked the tendency and skill to apply a notational approach to a less familiar situation or to interpret notational expressions within that situation. I propose the notion of “concept of representation” to explain the students’ work.

**Tomek Bartoszynski**, Boise State University

Title: On Applications of Set Theory

Date: Wednesday, 19 Sept 2001

Time: 3:40–4:30pm

Room: MG 118

Abstract: In this talk I will discuss several examples of statements that are neither provable nor disprovable, yet have the appearance of the ordinary mathematical propositions.