Some title

Some Person

USomething

Wednesday

Sept. 3, 2014

8:00-8:50am

Vincent Hall 313

Some Abstract. $e^x$

Coxeter transformation on cominuscule posets

Emine Yıldırım

UQAM

Friday

Sept. 15, 2017

3:35-4:25pm

Vincent Hall 570

Let $P$ be a cominuscule poset which can be thought of as a parabolic analogue of the poset of positive roots of a finite root system. Let $J(P)$ be the poset of order ideals of $P$. In this talk, we will investigate the periodicity of the Coxeter transformation on the poset $J(P)$, and show that the Coxeter transformation has finite order for two of the three infinite families of cominuscule posets, and the exceptional cases. Our motivation comes from a conjecture by Chapoton which states that the Coxeter transformation has finite order on the poset $J(R)$ when $R$ is the poset of positive roots of a finite root system. Our solution is formulated in representation theory of finite dimensional algebras, and we will further discuss the results within the same context.

Random Flag Complexes and Asymptotic Syzygies

Jay Yang

UWisconsin

Friday

Sept. 22, 2017

Vincent Hall 016

We use the probabilistic method to construct examples of conjectured phenomenon about asymptotic syzygies. In particular, we use the Stanley-Reisner ideals of random flag complexes to construct new examples of Ein and Lazarsfeld's nonvanishing for asymptotic syzygies and of Ein, Erman, and Lazarsfeld's conjectural on the asymptotic normal distribution of Betti numbers.

Cyclic symmetry in the Grassmannian

Steven Karp

Michigan

Friday

Sept. 29, 2017

3:35-4:25pm

Vincent Hall 570

The Grassmannian $Gr(k,n)$ is the space of $k$-planes in $C^n$. Its totally nonnegative part is the subset where all Plücker coordinates are real and nonnegative. There is a natural action of the cyclic group of order $n$ on $Gr(k,n)$ which preserves its totally nonnegative part. This 'cyclic symmetry' is prominent in the combinatorics of the totally nonnegative Grassmannian. I will discuss some surprising properties of the fixed points of the cyclic action. I will also present joint work with Pavel Galashin and Thomas Lam, which uses the cyclic action to show that the totally nonnegative part of $Gr(k,n)$ is homeomorphic to a ball.

Recent results in enumeration

Dennis Stanton

UMN

Friday

Oct. 6, 2017

3:35-4:25pm

Vincent Hall 570

I will survey some of my recent joint results in enumeration, including (1) integer partitions (2) enumeration over finite fields (3) orthogonal polynomials (4) posets. I will indicate open directions for each of these areas. No proofs will be given. This is joint work with Fulman, Guralnick, Ismail, Kim, Lewis, O’Hara, Rains, and Reiner.

Representation stability: A case study

Cihan Bahran

UMN

Friday

Oct. 13, 2017

3:35-4:25pm

Vincent Hall 570

The (ordered) configuration space of the complex plane has ties into various areas of mathematics. Church-Farb showed that, as the number of points in the configuration increases, the corresponding action of the symmetric group in cohomology "stabilizes" in a certain way. I will explain this phenomenon in the case of $H^1$ for the complex plane, and then talk about generalizations to other manifolds (Church) and some recent developments in the stable range.

Chip-firing for root systems

Sam Hopkins

MIT

Friday

Oct. 20, 2017

3:35-4:25pm

Vincent Hall 570

Propp recently introduced a variant of chip-firing on the infinite path where the chips are given distinct integer labels and conjecture that this process sorts certain (but not all) initial configurations of chips. Hopkins, McConville, and Propp proved Propp's sorting conjecture. We recast this result in terms of root systems: the labeled chip-firing game can be seen as a “vector-firing” process which allows the moves $\lambda \to \lambda + \alpha$ for $\alpha \in \Phi^+$ whenever $\langle \lambda, \alpha^\vee \rangle = 0$, where $\Phi^+$ is the set of positive roots of a root system of type $A_{2n-1}$. We give conjectures about confluence for this process in the general setting of an arbitrary root system. We show that the process is always confluent from any initial point after modding out by the action of the Weyl group (an analog of unlabeled chip-firing in arbitrary type). We also show that if we instead allow firing when $\langle \lambda, \alpha^\vee \rangle \in [-k-1,k-1]$ or $[-k,k-1]$, we always get confluence from any initial point. Moreover, in these two settings, the set of weights with given stabilization has a remarkable geometric structure related to permutohedra. This geometric structure leads us to define certain “Ehrhart-like” polynomials that conjecturally have nonnegative integer coefficients.

This is joint work with Pavel Galashin, Thomas McConville, and Alex Postnikov.

Component preserving mutations: building up maximal green sequences from sub-quivers

Eric Bucher

Michigan State

Friday

Oct. 27, 2017

3:35-4:25pm

Vincent Hall 570

Quiver mutation is a operation one can define on a directed graph that has shown to model the behavior of a large variety of mathematical objects. We will discuss a bit about quiver mutation, and the proceed to exploring quivers for a special sequence of mutations called maximal green sequences. The aim of the talk is to discuss recent work that allows one to build maximal green sequences for larger quivers by looking at "component preserving" sequences on induced subquivers. These new techniques have allowed us to construct maximal green sequences for large families of quivers where their existence was previously unknown.

Robinson-Schensted-Knuth via quiver representations

Hugh Thomas

UQAM

Friday

Nov. 3, 2017

3:35-4:25pm

Vincent Hall 570

The Robinson-Schensted-Knuth correspondence is a many-faceted jewel of algebraic combinatorics. In one variation, it provides a bijection between permutations of $n$ and pairs of standard Young tableaux with the same shape, which is a partition of $n$. In another (more general) version, it provides a bijection between fillings of a partition $\lambda$ by arbitrary non-negative integers and fillings of the same shape $\lambda$ by non-negative integers which weakly increase along rows and down columns (i.e., reverse plane partitions of shape $\lambda$). I will discuss an interpretation of RSK in terms of the representation theory of type $A$ quivers (i.e., directed graphs obtained by orienting a path graph). This allows us to generalize RSK to other Dynkin types (plus a choice of minuscule weight), and is related to periodicity results for piecewise-linear toggling. I will not assume familiarity with either RSK or with quiver representations. This is joint work with Al Garver and Becky Patrias.

The Mullineux involution and wall-crossing for the rational Cherednik algebra

Galyna Dobrovolska

Columbia

Friday

Nov. 10, 2017

3:35-4:25pm

Vincent Hall 570

The Mullineux involution on $p$-regular Young diagrams corresponds to the operation of taking the tensor product with the sign representation on modules for the symmetric group in characteristic $p$. In my talk I will report on some results towards proving R. Bezrukavnikov's conjectures on wall-crossing for the rational Cherednik algebra in positive characteristic, which was linked to the Mullineux involution by I. Loseu.

Identities for symmetric skew Grothendieck polynomials

Damir Yeliussizov

UCLA

Friday

Nov. 17, 2017

3:35-4:25pm

Vincent Hall 570

Symmetric Grothendieck polynomials can be viewed as an analog of Schur polynomials for the K-theory of Grassmannians. I will present various properties and applications for dual families of skew Grothendieck polynomials, such as skew Cauchy identities, skew Pieri rules, dual filtered Young graphs, generating series identities, some probabilistic models, and enumerative results.

Friday

Nov. 24, 2017

TBA

Vladimir Baranovsky

UC Irvine

Friday

Dec. 1, 2017

3:35-4:25pm

Vincent Hall 570

TBA

TBA

Nick Early

UMN

Friday

Dec. 8, 2017

3:35-4:25pm

Vincent Hall 570

TBA

Folding and dominance: relationships among mutation fans for surfaces and orbifolds

Shira Viel

NCSU

Friday

Dec. 15, 2017

3:35-4:25pm

Vincent Hall 570

The $n$-associahedron is a well-known $n$-dimensional polytope whose vertices are labeled by triangulations of an $(n+3)$-gon with edges given by diagonal flips. The $n$-cyclohedron is defined analogously using centrally-symmetric triangulations of a $(2n+2)$-gon, or, modding out by the symmetry, triangulations of an $(n+1)$-gon with one orbifold point. The polytopes can be realized in such a way that their normal fans are the ``$\mathbf{g}$-vector fans," or ``mutation fans," for certain cluster algebras. In this talk I will justify and generalize two relationships which hold between these fans: the normal fan to the $n$-cyclohedron can be obtained by intersecting the normal fan to the $(2n-1)$-associahedron with a certain subspace, and the normal fan to the $n$-cyclohedron refines the normal fan to the $n$-associahedron. I will show that these relationships are instances of ``folding" and ``dominance," respectively, and hold more generally for mutation fans for cluster algebras modeled by surfaces and orbifolds.

TBA

Tair Akhmejanov

Cornell

Friday

Jan. 19, 2018

3:35-4:25pm

Vincent Hall 570

TBA

TBA

TBA

TBA

Friday

Jan. 26, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Hanbaek Lyu

Ohio State

Friday

Feb. 2, 2018

3:35-4:25pm

Vincent Hall 570

TBA

TBA

TBA

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Friday

Feb. 9, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Friday

Feb. 16, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Alexander Garver

UQAM

Friday

Feb. 23, 2018

3:35-4:25pm

Vincent Hall 570

TBA

TBA

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TBA

Friday

Mar. 2, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Friday

Mar. 9, 2018

3:35-4:25pm

Vincent Hall 570

TBA

Friday

Mar. 16, 2018

TBA

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Friday

Mar. 23, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Friday

Mar. 30, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Linhui Shen

Michigan State

Friday

Apr. 6, 2018

3:35-4:25pm

Vincent Hall 570

TBA

TBA

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TBA

Friday

Apr. 13, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Friday

Apr. 20, 2018

3:35-4:25pm

Vincent Hall 570

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Friday

Apr. 27, 2018

3:35-4:25pm

Vincent Hall 570

TBA

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Friday

May 4, 2018

3:35-4:25pm

Vincent Hall 570

TBA

- Seminar meets on Fridays 3:35–4:25 in room 570 of Vincent Hall.
- Seminar announcement list sign-up.
- Organizers: Gregg Musiker (Fall), Pavlo Pylyavskyy (Spring) and Mike Chmutov. Website maintained by Mike Chmutov.
- Past seminar archive.
- Student Combinatorics Seminar.