Jens Harlander‘s interests are combinatorial topology and geometric group theory, with applications in 2- and 3-dimensional CW-complexes and manifolds. He is presently working on Whitehead’s asphericity conjecture, and on geometric realization problems, such as the Eilenberg–Ganea conjecture.
Uwe Kaiser‘s interests are the topology of manifolds, including embeddings, immersions and singularities of maps; in particular 3-dimensional topology: theory of knots and links, quantum topology; related homotopy theory and algebra. He is presently working on topological quantum field theories and categorification.
Doug Bullock‘s research is on skein modules. He presently holds the position of Associate Dean, and is also working on various projects in education and curriculum development.
Zach Teitler‘s interests include a range of problems in the areas of algebraic geometry and commutative algebra, usually with a combinatorial or computational flavor, including: arrangements (of hyperplanes, points, etc); multiplier ideals (computation, applications to commutative algebra); secant varieties, computing rank, and Hilbert functions; and computer experimentation in mathematics.
|Thomas Glass||Tube Equivalence of Spanning Surfaces and Seifert Surfaces||2008||Uwe Kaiser||Shasta College|
|Bailey Ross||Combinatorics and topology of curves and knots||2010||Jens Harlander||Boise State|
|Andrew Misseldine||Stably free modules over the Klein bottle group||2010||Jens Harlander||BYU Ph.D. program|
|Nick Davidson||Modules over localized group rings for groups mapping onto free groups||2011||Jens Harlander||U. Oregon Ph.D. program|
|Rachel Byrd||On the Geometry of Virtual Knots||2012||Jens Harlander||Ohio State University Ph.D. program|
|Kylee Zebedeo||Regular Homotopy of Closed Curves on Surfaces||2012||Uwe Kaiser||Clearwater Analytics|
|Tyler Allyn||Diagrammatically reducible 2-complexes||2014||Jens Harlander|
|Philip W. Hart||Monodromy representation of the braid group||2015||Uwe Kaiser||Boise State University|
|Monica Josue Agana||Classical theory of rearrangements||2015||Zach Teitler (co-advisor: Andres Caicedo)|
|Anna Marie Megale||The Frobenius problem||2015||Zach Teitler||Clearwater Analytics|
|Stuart Nygard||The density topology on the reals and other spaces||2016||Zach Teitler||Micron|
Members of the topology and geometry group organize two seminars, including the Topology Seminar and (together with members of the Cryptology Group) the Algebra, Geometry, Cryptology Seminar. Students are welcome to participate in these activities.
Graduate courses related to our research group include
- MATH 505/506, Abstract Algebra and Advanced Algebra
- MATH 511/512, Introduction to Topology and Advanced Topology
- MATH 582, Topics in Topology
- MATH 584, Topics in Computational Algebra
Lecture Notes on Differential Topology from a previous graduate course.
Jens Harlander and F. Rudolf Beyl organized the International Seminar on Low-Dimensional Homotopy Theory and Combinatorial Group Theory at the Wallowa Lake Lodge in Joseph, Oregon, in 2009.
Uwe Kaiser has organized Special Sessions at several recent regional AMS meetings, e.g. in 2006 a meeting on Floer homology and applications in Salt Lake City/UT (joint with Alexander Felshtyn), and in 2005 on the Algebraic Topology of Representation Varieties in Eugene/OR. He also organized a Special Session at the International AMS conference in Mainz and several International Topology Conferences in Germany. The geometric topology group also hosts the Cascade Topology Seminar about every third year.
Zach Teitler has organized several regional meetings and conference sessions, including AGIL’06 and AGIL’07, regional meetings for Algebraic Geometry In Louisiana (co-organized with Al Vitter); Special Session on Algebraic Geometry of Matrices and Determinants at a regional AMS meeting in Baton Rouge, LA, in 2008 (co-organized with Kent Neuerburg); Special Session on Computational Algebra and Convexity at a national AMS meeting in Washington, DC, in 2009 (co-organized with Dan Bates, Tsung-Lin Lee, and Sonja Petrovic); Special Session on Computational and Algorithmic Algebraic Geometry at a regional AMS meeting in Salt Lake City, UT, in 2011 (co-organized with Jim Wolper); Special Session on Combinatorial and Computational Commutative Algebra and Algebraic Geometry at a regional AMS meeting in Boulder in 2013 (co-organized with Hiro Abo and Alex Woo); Macaulay2 workshop at Boise State University in May 2015; Special session on Tensor decompositions and secant varieties at the Joint Mathematics Meetings in 2016; Special Session on Combinatorial and Computational Commutative Algebra and Algebraic Geometry at a regional AMS meeting in Salt Lake City in 2016 (co-organized with Hiro Abo, Jim Wolper, and Alex Woo).