Spring 2020

- This semester the Combinatorics Seminar meets on
**Fridays**in**Snow 306**from**3-4pm**. - Please contact Jeremy Martin or Federico Castillo if you are interested in speaking.
- Good general seminar-attending advice, especially for graduate students: The "Three Things" Exercise for getting things out of talks by Ravi Vakil

**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