Topology and Algebra at Boise State University
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.
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 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.
Topology and algebra graduate students
|Position after graduation
|Tube Equivalence of Spanning Surfaces and Seifert Surfaces
|Combinatorics and topology of curves and knots
|Stably free modules over the Klein bottle group
|BYU Ph.D. program
|Modules over localized group rings for groups mapping onto free groups
|U. Oregon Ph.D. program
|On the Geometry of Virtual Knots
|Ohio State University Ph.D. program
|Regular Homotopy of Closed Curves on Surfaces
|Diagrammatically reducible 2-complexes
|Professional and competitive kayaking; Altai Visuals
|Philip W. Hart
|Monodromy representation of the braid group
|Boise State University
|Monica Josue Agana
|Classical theory of rearrangements
|Zach Teitler (co-advisor: Andres Caicedo)
|Anna Marie Megale
|The Frobenius problem
|The density topology on the reals and other spaces
|On the Fundamental Group of Plane Curve Complements
|The Directed Forest Complex of Cayley Graphs
|K. Summer Ware
|Analytic Solutions for Diffusion on Path Graphs and Its Application to the Modeling of the Evolution of Electrically Indiscernible Conformational States of Lysenin
|Western New Mexico University
|Max Brian Sullivan
Topology and algebra undergraduate students
|Senior Thesis Title
|Position after graduation
|A brief encounter with linear codes
|Bishop Kelly High School
|Complementary Coffee Cups
|From Rings to Graphs: A Different Look at Structure
|Hyperbolic Geometry: History, Models, and Art
|An Exploration of the Chromatic Polynomial
|University of Idaho Ph.D. program
|The Cayley-Bacharach Theorem
|Boise State University M.S. program
|A Study of the Four Color Theorem
|Waring rank’s utility in optimizing algorithms involving point evaluations of homogeneous polynomials
|Partially Ordered Sets
|Premera Blue Cross
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.