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seminars:comb:start

# Combinatorics Seminar

## SPRING 2020

Organizers: Laura Anderson, Michael Dobbins, Benjamin Schröter, and Thomas Zaslavsky.

• Tuesday, January 21
Virtual Combinatorics Colloquium
Title: The First Bijective Proof of the ASM Theorem
Time: 2:00 - 3:00 (Note special time), preceded by a brief organizational meeting at 1:40
Room: WH-100E

• Tuesday, January 28
No meeting today; we're all too busy.

• Tuesday, February 4
Speaker: Laura Anderson (Binghamton)
Title: A Charming Conjecture Coming From Mathematical Psychology
Time: 1:15 - 2:15
Room: WH-100E

In joint work with John Dunn I've been trying to establish whether two types of psychological model are actually equivalent. The problem reduces to a simple, purely combinatorial question about patterns among inequalities in a rectangular array of numbers. I don't know the answer to the question: this talk is my shameless effort to recruit some help.

• Tuesday, February 11
Speaker: Michael Dobbins (Binghamton)
Title: The Real RAM Analogue to the Cook--Levin Theorem
Time: 1:15 - 2:15
Room: WH-100E

In “A Framework for robust realistic geometric computations” by Erickson, van der Hoog, and Miltzow, the authors introduce a real analog of NP defined as those decision problems where every positive instance has a witness consisting of both bits and real numbers that can be verified in polynomial time in the real RAM model of computation. They show that such a problem can be reduced in polynomial time on a Turing machine to deciding whether a multivariate polynomial formula has a real solution. This is analogous to the Cook–Levin Theorem, which shows that every problem in NP can be reduced in polynomial time to deciding whether a Boolean formula has a satisfying assignment.

• Tuesday, February 18
No meeting today; we're warming up for next week's exciting talk.

• Tuesday, February 25
Speaker: Ed Swartz (Cornell)
Title: Polymatroids are to Finite Groups as Matroids are to Finite Fields
Time: 1:15 - 2:15
Room: WH-100E

In 1935 Whitney introduced matroids as a combinatorial abstraction of linear independence. Since then there has been a strong connection between matroids, and the geometry and combinatorics of finite dimensional vector spaces over finite fields. Polymatroids are a very simply defined generalization of matroids. I will try to convince the audience that the title is nowhere near as crazy as it sounds. I will take classic examples of how matroids and vector spaces over finite fields interact, and show that they are special cases of how polymatroids and finite groups interact.

• Tuesday, March 3
No meeting today.

• Tuesday, March 10
Speaker: Chris Eppolito (Binghamton)
Title: Extension Spaces of Strongly Euclidean Oriented Matroids
Time: 1:15 - 2:15
Room: WH-100E

Following work of B. Sturmfels and G. Ziegler, I give a proof that the extension space of a strongly euclidean oriented matroid of rank $r$ is homotopy equivalent to the $(r-1)$-sphere.

• Tuesday, March 17
Speaker: Casey Donoven (Binghamton)
Title: Intersection Numbers and Minimal Subbases
Time: 1:15 - 2:15
Location: https://binghamton.zoom.us/j/951503518

Given a finite semigroup $S$, define $\Phi(S)$ to be the intersection of all maximal subsemigroups of $S$, also known as the Frattini subsemigroup of $S$. The intersection number of $S$ is the minimum number of maximal subsemigroups whose intersection is $\Phi(S)$. I will speak about a particular example of a semigroup with an interesting intersection number. In this example, the intersection number is equivalent to the minimum size of a subbasis of the discrete topology on a finite set, which is known.

The seminar will exist exclusively online, via Zoom. Casey will open the Zoom meeting at 1:00 to give time to work out any technical difficulties.

• [Tuesday, March 24] POSTPONED: new date will be announced
Speaker: Olakunle Abawonse (Binghamton)
Title: Homeomorphism Types of the Combinatorial Grassmannian MacP(2,n) and the Combinatorial Flag Manifold MacP(1,2,n)
Time: 1:15 - 2:15
Location: TBA

The Grassmannian manifold G(2,n) and flag manifold G(1, 2,n) are known to be homotopy equivalent to their respective combinatorial analogues MacP(2,n), MacP(1,2,n), which are simplicial complexes constructed from posets of oriented matroids and flags of oriented matroids. In this talk, I will prove that G(2,n) and G(1,2,n) are actually homeomorphic to these combinatorial analogues.

• Tuesday, March 31
No meeting today.

• Tuesday, April 7
Virtual Combinatorics Colloquium
Speaker: Maria Chudnovsky (Princeton)
Title: Recent Progress on the Erdos--Hajnal Conjecture
Time: 2:00 p.m.
Location: https://smcvt.zoom.us/j/831984515
What is the effect of excluding an induced subgraph on the global structure of a graph? While there do not seem to be general structural consequences, a conjecture of Erdos and Hajnal states that graphs with forbidden induced subgraphs behave very differently from general graphs; more precisely, they contain much larger cliques or stable sets. This conjecture is still open. I will discuss the history of this problem and some recent theorems related to it.

• Tuesday, April 14
Speaker:
Title:
Time: 1:15 - 2:15
Room: WH-100E

• Tuesday, April 21
Speaker: Amelia (Mattern) Cyr
Title: Deficiency in Signed Graphs
Time: 1:15 - 2:15, a break, and continuing for a while.
Location: Zoom meeting ID and link to be announced.
This is Ms. Cyr's doctoral dissertation defense. The examining committee consists of Laura Anderson, Michael Dobbins, Leslie Lander (outside examiner), and Thomas Zaslavsky (chair).
All are welcome to participate via Zoom.

• Saturday, April 25, 2020 (This will be online or postponed; to be decided.)
DISCRETE MATHEMATICS DAY at the University at Albany
Attendance is free. Preregistration (by April 15) helps them supply enough lunch. There are five invited talks, and a poster session that is open to everyone from undergraduates to retirees.

• Tuesday, April 28
Speaker:
Title:
Time: 1:15 - 2:15
Room: WH-100E

• Tuesday, May 5
Speaker: Ashley Wheeler (Mount Holyoke)
Title: TBA
Time: 1:15 - 2:15
Room: WH-100E

## Anticipated Future Talks

• Speaker: Daniel Slilaty (Wright State)
• Speaker: Christopher Hanusa (Queens College)
• Speaker: Bertrand Guenin (Waterloo)