The Math Department Colloquium features recent research of our faculty and our invited visitors.

*If you wish to be added to the department colloquium mailing list, or if you wish to give a colloquium talk, please contact the organizer Partha Mukherjee (parthamukherjee@boisestate.edu).*

Refreshments will be served in MB226 before each talk.

Archive of past math department colloquium abstracts

### Schedule for 2018–2019

**Doug Bullock**

Associate Professor and Associate Dean of COAS, Department of Mathematics, Boise State University

Title: *The Boise State Calculus Project*

Date: September 06 (Thursday), 2018

Time: 3:00–4:00 PM

Room: ILC 303

Abstract: I will describe the origins, motivation, implementation, results and impacts of a multi-year project to reshape the Calculus sequence at Boise State. The talk will be structured as a narrative, with research results presented at the points where they naturally emerged from the evolving project. Research results will fall into two categories:

• Institutional transformation and change management issues addressed during initial implementation and across subsequent project evolution.

• Natural experiments emerging from the project, measuring the project’s impact on success in Calculus, longitudinal performance in later courses, and retention at BSU or in major.

Restructuring of the traditional Calculus content and curriculum were a major part of the project. I will describe general themes of the curriculum changes, illustrated with specific examples. Although the project is effectively concluded, sustainability and future evolution will be discussed, time permitting.

**Joy Wright Whitenack**

Assistant Chair, Director of Undergraduate Studies, Associate Professor

Department of Mathematics, Virginia Commonwealth University

Title: *Coaching Middle School Mathematics Teachers: A Case for Emergent Professional Learning Communities*

Date: October 18 (Thursday), 2018

Time: 3:00–4:00 PM

Room: MB 139 (Math Building)

Abstract: In this presentation, I used mixed research methods to highlight the important role that coaches can play in supporting teacher learning and how these supports, in turn, correlated with student learning as measured by state achievement assessments. During the presentation, I will report results from statistical methods to address how teachers’ beliefs and students’ learning were positively affected because of their work with mathematics specialists. Against this backdrop, I will present findings of one case study of one specialist’s work with teachers to reconstruct the communities of practice that emerged as she and teachers engaged in this daily work. I then use these findings to argue for how particular practices sustained and contributed to a community that both support and engender teachers’ professional learning.

**Caroline Uhler**

Henry L. and Grace Doherty Associate Professor

Department of Electrical Engineering and Computer Science and Institute for Data, Systems and Society

Massachusetts Institute of Technology

Title: *From Causal Inference to Gene Regulation*

Date: January 31, 2019 (Thursday)

Time: 4:00–5:00 PM

Room: Remote broadcast in MB 139 (Math Building)

Abstract: A recent break-through in genomics makes it possible to perform perturbation experiments at a very large scale. The availability of such data motivates the development of a causal inference framework that is based on observational and interventional data. We first characterize the causal relationships that are identifiable from interventional data. In particular, we show that imperfect interventions, which only modify (i.e., without necessarily eliminating) the dependencies between targeted variables and their causes, provide the same causal information as perfect interventions, despite being less invasive. Second, we present the first provably consistent algorithm for learning a causal network from a mix of observational and interventional data. This requires us to develop new results in geometric combinatorics. In particular, we introduce DAG associahedra, a family of polytopes that extend the prominent graph associahedra to the directed setting. We end by discussing applications of this causal inference framework to the estimation of gene regulatory networks.

**Carl Pomerance**

John G. Kemeny Parents Professor Emeritus, Dartmouth College

Department of Mathematics, Dartmouth College

Title: *Primality Testing: Then and Now*

Date: February 20, 2019 (Wednesday)

Time: 3:00 – 4:00 PM

Room: Multipurpose Building, MPCB 108

Abstract: The task is simply stated. Given a large integer, decide if it is prime or composite. Gauss wrote of this algorithmic problem (and the twin task of factoring composites) in 1801: “the dignity of science itself

seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.” Though progress with factoring composites has been steady and substantial, I think Gauss would be

especially pleased with the enormous progress in primality testing, both in practice and in theory. In fact, one of the latest developments strangely and aptly employs a construct Gauss used to deal with ruler and compass constructions of regular polygons! This talk will present a survey of some of the principal ideas used in the prime recognition problem starting with the 19th century work of Lucas, to the 21st century work of Agrawal, Kayal, and Saxena, and beyond.

**Elisabeth Larsson**

Director at Department of Information Technology, Uppsala Multidisciplinary Centre for Advanced Computational Science, Senior lecturer at Department of Information Technology, Division of Scientific Computing

Uppsala University, Sweden

Title: *Exploring the radial basis function partition of unity method*

Date: March 04, 2019 (Monday)

Time: 3:00 – 4:00 PM

Room: ILC 202

Abstract: Radial basis function (RBF) methods are a relatively new class in the field of numerical methods for partial differential equations (PDEs). Researchers working with more established methods often ask if there really is a need to develop a new method. We can’t provide the definite answer to this question until we have tried successfully. In either case, the process of developing a method is a tool for gaining new knowledge, and this in itself is valuable. RBF methods provide a number of properties that make them attractive for PDEs, such as meshlessness, high order convergence rates for smooth problems, and ease of implementation. In this talk, we will follow the process of developing the radial basis function partition of unity method (RBF-PUM) with the objective of having these benefits. We demonstrate the success of the method through theory and experiments. Finally, we show recent and preliminary results from a project aimed at simulating the human respiratory system.

**Stephan Rosebrock**

Paedagogische Hochschule Karlsruhe, Germany

Title: *Finite topological spaces and simplicial complexes*

Date: March 07, 2019 (Thursday)

Time: 3:00 – 4:00 PM

Room: MB 135 (Math Building)

Abstract: Each partially ordered set X may be equipped with a topology induced by the partial order. It is possible to assign a finite simplicial complex K(X) to such an X, such that X and K(X) are weak homotopy equivalent. Conversely one can assign to each finite simplicial complex K a partially ordered set X such that X and K are weak homotopy equivalent. The talk starts with an introduction into finite topological spaces as developped by McCord, Stong, Barmak and others. We analyze when finite spaces are homotopy equivalent and introduce a notion of expansion and collapses for finite spaces. In the second part of the talk it will be shown how finite topological spaces may be used to prove results about simplicial complexes. I will show how long standing open questions in low dimensional topology and homotopy theory can be approached via finite topological spaces. The Andrews-Curtis conjecture and the Whitehead conjecture are reformulated for finite spaces and classes of examples are given for both conjectures which are not counterexamples.

**Kim Laine**

Researcher in the Cryptography Research Group

Microsoft Research, Redmond, WA

Title: *Homomorphic Encryption today: Schemes, Implementations, Applications*

Date: March 13, 2019 (Wednesday)

Time: 3:00 – 4:00 PM

Room: Multipurpose Building MPCB 118

Abstract: Homomorphic encryption is a powerful cryptographic technique that allows computation to be done directly on encrypted data. Since the first fully homomorphic encryption scheme was invented in 2009, the field has come a long way in terms of theory, implementations, and applications. Today there are multiple open-source implementations of fully homomorphic encryption available, including Microsoft SEAL, PALISADE by NJIT/Duality Cloud, and HElib by IBM Research. In this talk I will give a thorough overview of the state of homomorphic encryption: the audience will learn what homomorphic encryption is, why it is interesting, what works well, and what the main challenges are today.

**Steven Bleiler**

Professor

Fariborz Maseeh Department of Mathematics and Statistics

Portland State University

Title: *Probability, Stochasticity, and Repeated Games from the Quantum Viewpoint*

Date: April 18, 2019 (Thursday)

Time: 3:00 – 4:00 PM

Room: ILC 403

Abstract: The analysis of games played in the coming quantum computation environment is an exciting new area of research that spans the traditional areas of mathematical game theory, quantum mechanical physics and computer science. Fundamental to the study is the analysis of the possible advantage to players provided by the higher order of randomization in quantum mechanical systems as compared to that of classical systems. In this talk we will examine this phenomena in both finite and infinite stage repeated games, first in the context of history dependence where we’ll present a quantized version of the classical Parrando effect, i.e. where two losing games are combined via randomization to form a winning one. This will be followed by a brief overview of current research on the notion of quantum probability and the proper quantization of certain classical state dependent stochastic games, including the corresponding Markovian dynamics.

This talk is self contained and no previous knowledge of quantum mechanics or the game theory of history or state dependent games on the part of the audience will be assumed.

**David Gleich**

Jyoti and Aditya Mathur Associate Professor

Departments of Computer Science and Mathematics (Courtesy)

Purdue University

Title: *Higher-order clustering of complex networks*

Date: April 25, 2019 (Thursday)

Time: 5:00–6:00 PM

Room: Remote broadcast in MB 139 (Math Building)

Abstract: Spectral clustering is a well-known way to partition a graph or network into clusters or communities with provable guarantees on the quality of the clusters. This guarantee is known as the Cheeger inequality and it holds for undirected graphs. We’ll discuss a new generalization of the Cheeger inequality to higher-order structures in networks including network motifs. This is easy to implement and seamlessly generalizes spectral clustering to directed, signed, and many other types of complex networks. In particular, our generalization allow us to re-use the large history of existing ideas in spectral clustering including local methods, overlapping methods, and relationships with kernel k-means. We will illustrate the types of clusters or communities found by our new method in biological, neuroscience, ecological, transportation, and social networks.

Background papers and Code: https://arxiv.org/pdf/1612.08447.pdf (in Science, 2016), https://arxiv.org/abs/1704.05982 (at KDD2017), https://github.com/arbenson/higher-order-organization-julia

For those who can’t make it to MB 139, you can join the seminar from your computer, tablet or smartphone at

https://global.gotomeeting.com/join/501950733