## KU Combinatorics Seminar Spring 2018

The Combinatorics Seminar meets on Wednesdays in Snow 408 from 3-4pm.

Good general seminar-attending advice, especially for graduate students: The "Three Things" Exercise for getting things out of talks by Ravi Vakil

Our group project this semester is to read the expository article "Hodge Theory in Combinatorics" by Matt Baker, about the recent wotk of Karim Adiprasito, June Huh and Eric Katz. Some additional resources (provided by Federico Castillo):

Friday 1/19
Organizational Meeting

Wednesday 1/24
Joseph Doolittle
Partition Extenders

Abstract: In this talk, we will discuss partitions of simplicial complexes, and their relationship to the $$h$$-vector of the complex. We will show that while not every simplicial complex is partitionable, every simplicial complex does have a partition extender. This will allow a combinatorial interpretation of the h-vector of any pure simplicial complex. We further show some bounds on the size of a partition extender as well as some difficulties that arise when attempting to construct minimal partion extenders.

Wednesday 1/31
Federico Castillo
Hodge theory in combinatorics: an overview

Abstract: We take a general look into the recent proof (by Adiprasito-Huh-Katz) of Rota's conjecture that the absolute value of the coefficients in the characteristic polynomial of any matroid form a unimodal sequence. The main point is to explain what all of those word mean, to give examples, and to mention a thing or two about the proof, which uses ideas from Hodge theory.

Wednesday 2/7
Federico Castillo
The Chow ring of a matroid

Abstract: We continue with the definition of the Chow ring $$A(M)$$ of a matroid $$M$$. This is modeled on Chow rings of wonderful compactifications and toric varieties of Bergman fans. However, this admits a completely combinatorial description which is what allows to extend known results to the non representable case. The key property of this ring are the Hodge-Riemann relations, a concrete, linear algebra condition.

Wednesday 2/14
Jeremy Martin
The Chow ring of a matroid, II

Abstract: I'll give some geometric background (focusing more on ideas and less on technical specs) for what a Chow ring is, then we'll play around with the presentation of $$A(M)$$ for some specific examples.

Wednesday 2/21
Ken Duna
The Chow ring of a matroid, III CANCELLED; will be rescheduled

Wednesday 2/28
Bennet Goeckner
Title TBA (Preliminary Oral Exam for PhD)

Wednesday 3/7
TBA

Wednesday 3/14
Bruno Benedetti (University of Miami)
Title TBA

Wednesday 3/21
No seminar (Spring Break)

Wednesday 3/28
Jose Samper (University of Miami)
Title TBA

Wednesday 4/4
TBA

Wednesday 4/11
TBA

Wednesday 4/18
TBA

Wednesday 4/25
TBA

Wednesday 5/2
TBA

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

Last updated 2/21/18