# Bennet Goeckner

## Bennet Goeckner

In Fall 2018, I will be starting a postdoc at the University of Washington.

#### Contact Information:

Office: 647 Snow Hall

E-mail: bennet@ku.edu

#### Teaching:

- Math 126 - Calculus II - Spring 2018 -- All course information can be found on Blackboard.
- Last semester, I was a Graduate Research Consultant for Math 145, Honors Calculus I.

#### Office Hours:

Wednesday 12 PM - 1 PM

Also by appointment.

#### Research:

- My advisor is Jeremy Martin. I study algebraic and topological combinatorics, focusing on simplicial complexes and Stanley-Reisner theory. I am primarily interested in studying the interplay between algebraic, combinatorial, and topological properties of simplicial complexes, and how these properties imply various decompositions of the face poset.
- List of research articles:
- "Higher nerves of simplicial complexes." Joint with H. Dao, J. Doolittle, K. Duna, B. Holmes, and J. Lyle. Submitted for publication. arXiv:1710.06129
- "Universal partial words over non-binary alphabets." Joint with C. Groothuis, C. Hettle, B. Kell, P. Kirkpatrick, R. Hirsch, and R. Solava. To appear in Theoretical Computer Science. arXiv:1611.03928
- "A non-partitionable Cohen-Macaulay simplicial complex." Joint with A.M. Duval, C.J. Klivans, and J.L. Martin. Advances in Mathematics 299 (2016), 381-395; arXiv:1504.04279

- I served as the chair of the organizing committee for the Graduate Student Combinatorics Conference 2017, which was hosted at the University of Kansas April 7-9. The conference was funded by grants from the NSF, the Combinatorics Foundation, and the Department of Mathematics and College of Liberal Arts and Sciences at the University of Kansas. We had 107 participants in attendance, which makes GSCC 2017 the largest GSCC on record.

#### Recent and Upcoming Talks:

- "Stanley's diamond conjecture," Combinatorics Seminar, University of Kansas, September 22, 2017
- "Generalized nerves of simplicial complexes," Graduate Algebra Seminar, University of Kansas, September 19, 2017
- "Colorated homology and balanced complexes," Special Session on Geometric Combinatorics and Combinatorial Commutative Algebra, AMS Central Sectional, University of North Texas, September 10, 2017
- "Colorated homology and balanced complexes," Combinatorics Seminar, Kansas State University, March 1, 2017
- "A non-partitionable Cohen-Macaulay complex," Algebra-Geometry-Combinatorics Seminar, University of Illinois Urbana-Champaign, February 23, 2017

#### Other Math Activities:

- I am a Science Mentor for the newly-formed Frontiers for Young Minds, Mathematics, a mathematics journal targeted towards and edited by kids. I help children ages 8-15 review articles for publication.
- Each April, the University of Kansas celebrates Math Awareness Month with a variety of activities for elementary, middle, and high school students. I have been involved with KU's Math Awareness Month activities for the past four years, and I have served as the student organizer of the activity workshops for elementary school students for the past two years.