Some title

Some Person

USomething

Wednesday

Sept. 3, 2014

8:00-8:50am

Vincent Hall 313

Some Abstract. $e^x$

TBA

No seminar- 1st week of class

Friday

Sept. 7, 2018

3:35-4:25pm

Vincent Hall 570

No seminar- 1st week of class

Friday

Jan. 24, 2020

3:35-4:25pm

Vincent Hall 570

Weak order and descents for monotone triangles

Vic Reiner

Friday

Jan. 31, 2020

3:35-4:25pm

Vincent Hall 570

(joint work with Zach Hamaker; arXiv:1809.1057)
Monotone triangles are combinatorial objects in bijection with alternating sign matrices, a fascinating generalization of permutation matrices. We will review this connection, and the fact that strong Bruhat order on permutations has a natural extension to monotone triangles.
We will then explain an analogous extension of the weak Bruhat order on permutations to monotone triangles. This comes from extending the notions of descents in permutations and the "bubble-sorting" action of the 0-Hecke algebra on permutations to monotone triangles.
We will also explain one of our motivations: to give a natural family of shellings for Terwilliger's recently defined order on subsets.

Unconditional Reflexive Polytopes

McCabe Olsen

Ohio State

Friday

Feb. 7, 2020

3:35-4:25pm

Vincent Hall 570

A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets. This is joint work with Florian Kohl (Aalto University) and Raman Sanyal (Goethe Universität Frankfurt).

Combinatorics of the double-dimer model

Helen Jenne

Oregon

Friday

Feb. 14, 2020

3:35-4:25pm

Vincent Hall 570

In this talk we will discuss a new result about the
double-dimer model: under certain conditions, the partition function for
double-dimer configurations of a planar bipartite graph satisfies an
elegant recurrence, related to the Desnanot-Jacobi identity from linear
algebra. A similar identity for the number of dimer configurations (or
perfect matchings) of a graph was established nearly 20 years ago by Kuo
and others. We will also explain one of the motivations for this work,
which is a problem in Donaldson-Thomas and Pandharipande-Thomas theory
that will be the subject of a forthcoming paper with Gautam Webb and Ben
Young.

Separable elements and splittings of Weyl groups

Yibo Gao

MIT

Friday

Feb. 21, 2020

3:35-4:25pm

Vincent Hall 570

We introduce separable elements in finite Weyl groups, generalizing the well-studied class of separable permutations. They enjoy nice properties in the weak Bruhat order, enumerate faces of the graph associahedron of the corresponding Dynkin diagrams, and can be characterized by pattern avoidance in the sense of Billey and Postnikov. We then prove that the multiplication map $W/V \times V \to W$ for a generalized quotient of the symmetric group is always surjective when V is a principal order ideal, providing the first combinatorial proof of an inequality due originally to Sidorenko in 1991, answering an open problem of Morales, Pak, and Panova. We show that this multiplication map is a bijection if and only if V is an order ideal in the right weak order generated by a separable element, answering an open question of Björner and Wachs in 1988. This is joint work with Christian Gaetz.

Generalized snake graphs from orbifolds

Elizabeth Kelley

UMN

Friday

Feb. 28, 2020

3:35-4:25pm

Vincent Hall 570

Cluster algebras, as originally defined by Fomin and Zelevinsky, are characterized by binomial exchange relations. A natural generalization of cluster algebras, due to Chekhov and Shapiro, allows the exchange relations to have arbitrarily many terms. A subset of these generalized cluster algebras can be associated with triangulations of orbifolds, analogous to the subset of ordinary cluster algebras associated with triangulated surfaces. We generalize Musiker-Schiffler-Williams' snake graph construction for this subset of generalized cluster algebras, yielding explicit combinatorial formulas for the cluster variables. We then show that our construction can be extended to give expansions for generalized arcs on triangulated orbifolds. This is joint work with Esther Banaian.

TBA

Friday

Mar. 6, 2020

3:35-4:25pm

Vincent Hall 570

No seminar - Spring Break

Friday

Mar. 13, 2020

3:35-4:25pm

Vincent Hall 570

Gabriel Frieden

Friday

Mar. 20, 2020

3:35-4:25pm

Vincent Hall 570

TBA

Friday

Mar. 27, 2020

3:35-4:25pm

Vincent Hall 570

TBA

Friday

Apr. 3, 2020

3:35-4:25pm

Vincent Hall 570

TBA

Friday

Apr. 10, 2020

3:35-4:25pm

Vincent Hall 570

TBA

Friday

Apr. 17, 2020

3:35-4:25pm

Vincent Hall 570

TBA

Friday

Apr. 24, 2020

3:35-4:25pm

Vincent Hall 570

TBA

Friday

May 1, 2020

3:35-4:25pm

Vincent Hall 570

- Seminar meets on Fridays 3:35-4:25 in room 570 of Vincent Hall. The Fall 2019 seminar site is here.
- Seminar announcement list sign-up.
- Organizers: Chris Fraser and Vic Reiner.
- Past seminar archive.
- Student Combinatorics and Algebra Seminar; meets on Thursdays.