Combinatorics Undergraduate Research Seminar (FGCU-CUReS)
In 2018, Drs. Katie Johnson, Shaun Sullivan, and I formed the Combinatorics Undergraduate Research Seminar (FGCU-CUReS) to share our favorite mathematical theories and problems with FGCU students.
This semester we will start by introducing a combinatorial problem posed by Dr. Shaun Sullivan motivated by the many terrible drivers in Southwest Florida.
Time permitting we will also discuss how to count tetras tilings of the plane following methods introduced to us by Dr. Steve Butler.
Spring 2021 - Student Presentations
Florida Undergraduate Research Conference (FURC) March 26, 2021:
Markov Models for the tipsy cop and robber game on graphs (Viktoriya Bardenova and Vincent Ciarcia)
Spring 2020 - Lecture Notes on Umbral Calculus - led by Shaun Sullivan
FGCU Community Engagement & Research Day (CERD 2020)Domination Theory and the Placement of Solar Panels - Viktoriya Bardenova
Alyson Baumgardner, Brooklyn Crum
Morgan Bettencourt, Andrew Mckay, Carlton Saunderson
Here are some papers with CUReS students.
Fall 2019 Lecture Notes on Coxeter Groups - led by Erik Insko
Lecture 1 - Why study Coxeter groups? Slides
Lecture 2 - Presenting Coxeter groups. Slides
Lecture 4 - A "Cayley-esque" theorem and brainstorming approaches to the ADL conjecture. Slides
Lecture 6 - Inversion sets, Bruhat order, and a new conjecture involving pinnacle sets of permutations Slides
Lecture 7 - More on Bruhat Order, Counting using "q-analogues", and some proofs our Conjectures! Slides
Diaz-Lopez's Peak Set Palindromicity Conjecture that we explored in this seminar was recently resolved by Gaetz and Gao. See their preprint for elegant proofs of the palindromicity result and more open problems.
A formula for enumerating permutations with a fixed pinnacle set - this is joint work with Alexander Diaz-Lopez, Pamela Harris, Isabella Huang, and Lars Nilsen.
Fall 2018 Lecture Notes on Generating Functions - led by Dr. Shaun Sullivan