The Combinatorics Seminar meets on Wednesdays in Snow 408 from 3-4pm.
Please contact Jeremy Martin 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
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):
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.
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.
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.
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.
The Chow ring of a matroid, III CANCELLED; will be rescheduled
Title TBA (Preliminary Oral Exam for PhD)
Bruno Benedetti (University of Miami)
No seminar (Spring Break)
Jose Samper (University of Miami)
For seminars from previous semesters, please see the KU Combinatorics Group page.
Last updated 2/21/18