KU Combinatorics Seminar
Spring 2020

Friday 1/24
Organizational meeting

Friday 1/31
Jeremy Martin
Hopf Monoids - A Refresher

Abstract: This is an intentionally off-the-cuff talk, to simulate the answer I would give over coffee at a conference to the question, "So what are these things called Hopf monoids and what do you do with them?"

Friday 2/7
Federico Castillo
Hopf Algebras - Examples

Abstract: We are going to explore examples coming from group algebras, Lie algebras, symmetric functions, and posets. The goal is to see how Hopf algebras allow us to give a common framework for different situations. Title TBA

Friday 2/14
Shira Zerbib (Iowa State)
Colorful phenomena in discrete geometry and combinatorics via topological methods

Abstract: We will discuss two recent topological results and their applications to several different problems in discrete geometry and combinatorics involving colorful settings.

The first result is a polytopal-colorful generalization of the topological KKMS theorem due to Shapley. We apply this theorem to prove a colorful extension of the d-interval theorem of Tardos and Kaiser, as well as to provide a new proof to the colorful Caratheodory theorem due to Barany. Our theorem can be also applied to questions regarding fair-division of goods (e.g., multiple cakes) among a set of players. This is a joint work with Florian Frick.

The second result is a new topological lemma that is reminiscent of Sperner's lemma: instead of restricting the labels that can appear on each face of the simplex, our lemma considers labelings that enjoy a certain symmetry on the boundary of the simplex. We apply this to prove that the well-known envy-free division theorem of a cake is true even if the players are not assumed to prefer non-empty pieces, whenever the number of players is prime or equal to 4. This is joint with Frederic Meunier.

Friday 2/21
Bennet Goeckner (University of Washington)
Partition extenders and Simon's conjecture

Abstract: If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpretation in terms of any partitioning of the complex. Such an interpretation does not exist for non-partitionable complexes. Given a non-partitionable complex, we will construct a relative complex---called a partition extender---that allows us to write the h-vector of a non-partitionable complex as the difference of two h-vectors of partitionable complexes in a natural way. We will show that all pure complexes have partition extenders.

A similar notion can be defined for Cohen--Macaulay and shellable complexes. We will show precisely which complexes have Cohen--Macaulay extenders, and we will discuss a connection to a conjecture of Simon on the extendable shellability of uniform matroids. This is joint work with Joseph Doolittle and Alexander Lazar.

Friday 2/28
Kevin Marshall
Title TBA

Friday 3/6
TBA (we may cancel today)

Friday 3/13
No seminar (Spring Break)

Friday 3/20
Dylan Beck
Title TBA

Friday 3/27
Mark Denker
Title TBA

Friday 4/3
Trevor Arrigoni
Title TBA

Friday 4/10
Marge Bayer
Title TBA

Friday 4/17
Jose Bastidas (Cornell)
Title TBA

Friday 4/24
No seminar (get ready for GPCC 2020!)

Friday 5/1
Laura Escobar (Washington U. in St. Louis)
Title TBA

Friday 5/8
No seminar (Stop Day)

For seminars from previous semesters, please see the KU Combinatorics Group page.

Last updated Mon 2/10/20