Topology and Algebra at Boise State University

The Topology and Algebra Group consists of Jens Harlander, Uwe Kaiser, Doug Bullock, and Zach Teitler.

Research interests

Scott Andrews‘s interests are in the representation theory of finite groups. He is particularly interested in matrix groups over finite fields and how their representation theory relates to the ring of symmetric functions and other combinatorial objects.

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.

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.

Seminars

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.

Courses

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.

Graduate students

Student Thesis/Project Title Year Defended Advisor Position after graduation
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 Professional and competitive kayaking; Altai Visuals
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) Vacasa
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
Mitchell Scofield On the Fundamental Group of Plane Curve Complements 2019 Jens Harlander
Kennedy Courtney 2020 (exp.) Jens Harlander
Jake Weedn 2021 (exp.) Zach Teitler

Undergraduate students

Student Senior Thesis Title Year Advisor Position after graduation
Brent El-Bakri A brief encounter with linear codes 2014 Zach Teitler Bishop Kelly High School
Stacia Orr Cubik Mathemagic 22016 Zach Teitler
Brandon Sams Complementary Coffee Cups 2017 Zach Teitler
Kyle Auble From Rings to Graphs: A Different Look at Structure 2017 Zach Teitler
Karly Reid Hyperbolic Geometry: History, Models, and Art 2017 Zach Teitler Mathnasium
Amanda Aydelotte An Exploration of the Chromatic Polynomial 2017 Zach Teitler University of Idaho Ph.D. program
Kayla Neal The Cayley-Bacharach Theorem 2018 Zach Teitler Boise State University M.S. program
Sarah Alley A Study of the Four Color Theorem 2019 Scott Andrews

Conference organizing

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 additionally organized several regional meetings and conference sessions.