- MARIA CHUDNOVSKY, Princeton
Recent Progress on the Erdos-Hajnal Conjecture [PDF]
What is the effect of excluding an induced subgraph on the global
structure of a graph? While there do not seem to be general structural
consequences, a conjecture of Erdos and Hajnal states that graphs with
forbidden induced subgraphs behave very differently from general graphs; more
precisely they contain much larger cliques or stable sets. This conjecture is
still open. In this talk we will discuss the history of this problem and some
recent theorems related to it.
- SARAH MAYES-TANG, University of Toronto
Listening Before Teaching: Building mathematical understanding by understanding our students [PDF]
Despite generations of curricular reforms and investments in outreach activities, mathematics remains one of the most misunderstood fields of study. Tied to this problem of reputation is a representation problem: the numbers of women and those from racial minorities are still unacceptably low in math, especially at the senior ranks. How can we make progress towards solving the dual reputation and representation problems that face math? I will discuss recent research in the social sciences that points towards the importance of listening to and understanding our students and mentees at all levels, from grade school through grad school. I will give examples of concrete practices that build understanding by first understanding students and discuss how listening has played a key role in recent innovations to an introductory calculus program at the University of Toronto.
- ANTONIO MONTALBAN, University of California, Berkeley
A Robuster Scott Rank [PDF]
The Scott rank was introduced in the 60's as measure of complexity for algebraic structures. There are various other ways to measure the complexity of structures that give ordinals that are close to each other, but are not necessarily equal. We will introduce a new definition of Scott rank where all these different ways of measuring complexity always match, obtaining what the author believes it the correct definition of Scott Rank.
We won't assume any background in logic, and the talk will consist mostly of an introduction to these topics.
- KIRSTEN MORRIS, Waterloo
- MALABIKA PRAMANIK, UBC
- LAUREN WILLIAMS, Harvard
Probability and combinatorics: hopping particles and Macdonald polynomials [PDF]
The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice. It was initially introduced by Macdonald-Gibbs-Pipkin to provide a model for translation in protein synthesis. On the other hand, Macdonald polynomials are a remarkable family of multivariate polynomials which generalize Schur polynomials and Hall-Littlewood polynomials. I’ll explain how the study of the ASEP on a ring leads to new formulas for Macdonald polynomials.