Skip to main content

Topology and Algebra at Boise State University

The Topology and Algebra Group consists of Scott Andrews, Jens Harlander, Uwe KaiserZach 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.

Intersecting yellow disks with red, blue, and green lines

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

A point and a line intersect a series of overlapping planes labeled E1, E2, E3, and E4

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 and 506, Abstract Algebra and Advanced Algebra
  • MATH 511 and 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

Topology and algebra graduate students

StudentThesis/Project TitleYear DefendedAdvisorPosition after graduation
Thomas GlassTube Equivalence of Spanning Surfaces and Seifert Surfaces2008Uwe KaiserShasta College
Bailey RossCombinatorics and topology of curves and knots2010Jens HarlanderBoise State
Andrew MisseldineStably free modules over the Klein bottle group2010Jens HarlanderBYU Ph.D. program
Nick DavidsonModules over localized group rings for groups mapping onto free groups2011Jens HarlanderU. Oregon Ph.D. program
Rachel ByrdOn the Geometry of Virtual Knots2012Jens HarlanderOhio State University Ph.D. program
Kylee ZebedeoRegular Homotopy of Closed Curves on Surfaces2012Uwe KaiserClearwater Analytics
Tyler AllynDiagrammatically reducible 2-complexes2014Jens HarlanderProfessional and competitive kayaking; Altai Visuals
Philip W. HartMonodromy representation of the braid group2015Uwe KaiserBoise State University
Monica Josue AganaClassical theory of rearrangements2015Zach Teitler (co-advisor: Andres Caicedo)Vacasa
Anna Marie MegaleThe Frobenius problem2015Zach TeitlerClearwater Analytics
Stuart NygardThe density topology on the reals and other spaces2016Zach TeitlerMicron
Mitchell ScofieldOn the Fundamental Group of Plane Curve Complements2019Jens Harlander
Kennedy CourtneyThe Directed Forest Complex of Cayley Graphs2020Jens HarlanderBoise State
K. Summer WareAnalytic Solutions for Diffusion on Path Graphs and Its Application to the Modeling of the Evolution of Electrically Indiscernible Conformational States of Lysenin2020Uwe Kaiser
Sarah SchottExploring the Beginnings of Algebraic K-Theory2021Jens HarlanderWestern New Mexico University
Max Brian SullivanWaring Rank and Apolarity of Some Symmetric Polynomials2022Zach Teitler
Alex Byars2023 (exp)Jens Harlander
Emma Weaver2023 (exp)Jens Harlander
Austin Fender2024 (exp)Uwe Kaiser

Undergraduate students

Topology and algebra undergraduate students

StudentSenior Thesis TitleYearAdvisorPosition after graduation
Brent El-BakriA brief encounter with linear codes2014Zach Teitler
Stacia OrrCubik Mathemagic2016Zach Teitler
Brandon SamsComplementary Coffee Cups2017Zach Teitler
Kyle AubleFrom Rings to Graphs: A Different Look at StructureZach Teitler
Karly ReidHyperbolic Geometry: History, Models, and ArtZach TeitlerMathnasium
Amanda AydelotteAn Exploration of the Chromatic Polynomial2017Zach TeitlerUniversity of Idaho Ph.D. program
Kayla NealThe Cayley-Bacharach TheoremZach TeitlerBoise State University M.S. program
Sarah AlleyA Study of the Four Color TheoremScott Andrews
Tyler WareWaring rank’s utility in optimizing algorithms involving point evaluations of homogeneous polynomialsZach Teitler
Sarah Hall Permutation StatisticsZach TeitlerClearwater Analytics
Miranda SchaefferPartially Ordered Sets2021Zach TeitlerPremera Blue Cross

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.