Fall 2023

Putnam Post Mortem

Speaker: Noam Elkies

Abstract: Join our own Professor Noam Elkies to discuss a selection of this year’s Putnam problems

Bender-Knuth Billiards in Coxeter Groups

Speaker: Eliot Hodges

Abstract: Abstract: In this talk, which will be accessible to undergraduates of all levels, we discuss the way in which Schützenberger's famous promotion map--a permutation of the linear extensions of a poset--can be generalized to a combinatorial sorting operator on Coxeter groups. We also give a description of this Coxeter-theoretic promotion in terms of (noninvertible) Bender-Knuth toggles, which generalize Bender-Knuth involutions to Coxeter groups. In addition to classifying many of the cases where promotion will "sort" (such Coxeter groups are dubbed futuristic), we describe an alternate, more geometric way of thinking about the problem, in which we have a black hole and a beam of light traveling through (or reflecting off of) a series of one-way mirrors. (This talk includes joint work with Barkley, Defant, Kravitz, and Lee.)

3D Tic-Tac-Toe

Speaker: Yanni Raymond

Abstract: If you ever spent an afternoon of your childhood playing tic-tac-toe, you may have noticed that the game typically ends in a draw. Indeed, with optimal play from both players, the game will be a draw. But what about tic-tac-toe played on different board sizes, or in more than two dimensions? This talk will introduce pairing strategies, strategy stealing, and the Erdös-Selfridge theorem to resolve planar tic-tac-toe and introduce hypercube tic-tac-toe.

Peg Solitaire on Graphs with Large Diameter

Speaker: Daniel Sheremeta

Abstract: Peg solitaire is a classical table game played on a variety of different boards. In this talk, we explore the generalisation of peg solitaire to arbitrary graphs, which was proposed as early as 1994 by Moulton. Based on research that I did at Harvard this summer, the talk’s focus is on the solvability (i.e. whether all of the pegs can be removed) of graphs with a large number of edges. I hope to keep things extremely accessible, assuming only a familiarity with the basic vocabulary of graph theory.

Combinatorics of Crystal Graphs

Speaker: Jack Mann

Abstract: Crystal graphs are a useful tool to have when working with representations of quantum groups. While quantum groups are complex algebraic structures, we can represent elements in their representations as Young tableaux. With this method, we can develop a more abstract understanding of its algebraic structure using counting strategies. In this talk, we examine the crystal graph corresponding to the symplectic Lie algebra and look for patterns in the arrangement of crystals and their weights, aiming to find the dimensions of subspaces in the corresponding representation.

Game of Cones: Jeu de Taquin and Simplicial Complexes

Speaker: Dora Woodruff

Abstract: In this talk, we will explore a connection between topology and combinatorics. To every partially ordered set, objects often studied by combinatorialists, one can assign a simplicial complex and study its topological properties. For example, a theorem of Björner says that whenever the partially ordered set is a lattice, the resulting complex is homeomorphic to a ball. We'll start by discussing this classical theory, and then explore a new direction that brings in another combinatorial player: Young tableaux. Based on some research I did this summer, a meta-theme of this talk will also be that it's not always terrible news when your conjectures are wrong!

ob Panel

Please join us for a panel discussion about what careers and jobs you can pursue with a background in mathematics. Our panelists are 

• Sarah Minucci, Senior Scientist - Mathematical Modeler at Applied BioMath .

• Aiden Carey, Software Engineer at Klaviyo.

• Heemyung Hwang, Software Engineer at Zagaran.

• Vasily Ilin, Data Engineer at Google.

Do you know a proof of the fundamental theorem of algebra?

Speaker: Cliff Taubes, Harvard University

Abstract: The fundamental theorem of algebra (d’Alembert’s theorem) says that any monic polynomial of degree n has n roots counting multiplicity.  There are lots of proofs—but which is the simplest?  And, what do you need to know to prove it?