## Spring 2024

**Seminar on Algebraic Combinatorics****Benjamin Dequêne (University of Picardie Jules Verne): A generalized RSK correspondence via the combinatorics of (type A) quiver representations**

Organizer: Emily Gunawan, email: emily_gunawan@uml.edu

January 24, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: The Robinson-Schensted-Knuth (RSK) correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableau. A generalized version of RSK gives a bijection from fillings of a tableau of shape lambda to reverse plane partitions of shape lambda.

From the quiver representation point of view, the RSK correspondence provides a transformation between two different invariants of a module X (in a certain subcategory). The entries in the arbitrary filling of shape lambda correspond to multiplicities of indecomposable summands of the representation, while the entries in the reverse plane partition of shape lambda record the generic Jordan form data of X, an invariant introduced by Garver, Patrias and Thomas.

My talk aims to present a version of RSK that works from the most general possible choice of a subcategory of the category of representations of a type A quiver. Note that this talk will not assume that the audience has prior knowledge of quiver representations.

This is a combinatorial extraction (in progress) of my Ph.D. work, supervised by Hugh Thomas.

**Seminar: Working on What (WOW)****Daniel Glasscock (UMass Lowell): Difference sets: not Bohring but potentially Bohr**

Organizer: Emily Gunawan, email: emily_gunawan@uml.edu

February 21, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: It is a basic and often useful fact in analysis that convolutions make things smoother. Less famous is the additive combinatorial analogue: set sums and differences support richer structures (and, hence, are “smoother”). This fact – known almost a century ago – is still being refined and finding new applications in additive number theory today. And there are still many open questions. In this talk, we will discuss the following open question: must the difference set A-A of a syndetic subset of integers A contain a Bohr set?

**Seminar: Working on What (WOW)****Amanda Redlich (UMass Lowell): Eeny-Meeny-Miney-Moe: Random approaches to solving hard problems**

Organizer: Emily Gunawan, email: emily_gunawan@uml.edu

March 20, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: Some problems seem impossibly hard: computing the Ramsey number R(5,5), modeling the internet, picking a grocery store checkout line. It turns out that using random guesses is a great approach to all three of these! A lot of my research uses randomized algorithms and the probabilistic method. In this talk I'll give an overview of some of the classical results in the area.

**Seminar on Analysis and Applications****Yuan Liu (Wichita State University): High order structure-preserving numerical methods for convection-diffusion-reaction equations**

Organizer: Shiwen Zhang, email: shiwen_zhang@uml.edu

April 1, 11 a.m. - Noon, Room: Southwick Hall 350W

Abstract: Convection-diffusion-reaction (CDR) equation is one of the widely used mathematical models in science and engineering. It describes how one or more substances distributed under the influences of convection, diffusion and reaction processes. In this talk, we will present some recent work on high order numerical methods for solving CDR equation under two cases. (1) When there are only convection terms, the CDR equation is hyperbolic conservation laws. We will talk about the development of high order bound-preserving numerical methods. (2) When there are only diffusion and reaction terms, Krylov implicit integration factor discontinuous Galerkin methods on sparse grids are proposed to solve the equation in high dimensional cases.

**Seminar: Working on What (WOW)****Tibor Beke (UMass Lowell): Hex**

Organizer: Emily Gunawan, email: emily_gunawan@uml.edu

April 24, 11 a.m. - Noon, Room: Southwick Hall 350W

The game of Hex, invented by Danish polymath Piet Hein and (later but independently) future Nobel Prize winner John Nash is exceptional in being at the same time ...

- a thoroughly enjoyable board game
- a case study in taking the continuum limit of a discrete theorem (the fact that no Hex game can end in a draw is "equivalent" to the Brouwer Fixed Point theorem)
- a case study in game theory (the so-called "strategy stealing" argument proves that the first player has a winning strategy)
- a case study in computational complexity (finding the winning move is PSPACE-complete, probably explaining why no explicit winning strategy has been found beyond 10x10 boards).