# Topology and Algebra at Boise State University

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

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 | The Directed Forest Complex of Cayley Graphs | 2020 | Jens Harlander | Boise State |

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 | 2020 | Uwe Kaiser | |

Sarah Schott | 2021 | Jens Harlander | Western New Mexico University | |

Max Brian Sullivan | 2022 | Zach Teitler | ||

Alex Byars | 2023 (exp) | Jens Harlander | ||

Emma Weaver | 2023 (exp) | Jens Harlander | ||

Austin Fender | 2024 (exp) | Uwe Kaiser |

## Undergraduate students

Topology and algebra 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 | |

Tyler Ware | Waring rank’s utility in optimizing algorithms involving point evaluations of homogeneous polynomials | 2021 | Zach Teitler | |

Sarah Hall | Permutation Statistics | 2021 | Zach Teitler | Clearwater Analytics |

Miranda Schaeffer | Partially Ordered Sets | 2021 | Zach Teitler | Premera 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.