Mathematics Graduate Students Organization

Seminar:

Date: September 18

C. Yan: "Enumerative Combinatorics with Fillings of Polyominoes"

Abstract: An important and active area of Enumerative Combinatorics is the study of combinatorial statistics, which are simply functions from the combinatorial objects to the set of non-negative integers. Many interesting statistics have been investigated over families of combinatorial structures, such as permutations, words, matchings, set partitions, integer sequences, graphs, and multi-graphs. In this talk I will introduce a new combinatorial model, fillings of polyominoes, which provides a unified approach to the classical combinatorial analysis on all the above mentioned structures. I will discuss some recent results and open problems related to this model.

A. Shiu: "What is the Global Attractor Conjecture? "

Abstract: First posed forty years ago, the Global Attractor Conjecture posits that the dynamical systems arising from a certain class of chemical reaction networks are globally stable. In this mini-talk, I will give a history of this conjecture and describe how ideas from algebra and polyhedral geometry have contributed in recent years toward its partial resolution.