Past Events

Abstract: Given a finite graph, the arboreal gas is the measure on forests (subgraphs without cycles) in which each edge is weighted by a parameter β>0. Equivalently this model is bond percolation conditioned to be a forest, the independent sets of...

In 1975, the physicists Imry and Ma predicted that the incorporation of a random field in low-dimensional spin systems leads to the rounding of first-order phase transitions. These predictions were rigorously established by Aizenman and Wehr in 1989...

I will present a work in progress. In 1954, Tutte proved flow-colouring duality and made a conjecture that every graph without a cut-edge has a nowhere-zero 5-flow. A parallel conjecture to this, but for signed graphs is Bouchet's conjecture (1983)...

We will discuss several SIS-PDE models, focusing on the effects of spatial movement and time-periodicity of environment, the role of exposed populations, and the interaction of multiple strains.

Khovanov homology, though relatively young, is difficult to survey in an hour. This talk will nevertheless attempt to do so, by focussing on the problem of characterizing thin links—those links with simplest-possible Khovanov homology. This is a...

I will give an overview of a few places where combinatorial structures have an interesting role to play in quantum field theory and which I have been involved in to varying degrees, from the Connes-Kreimer Hopf algebra and other renormalization Hopf...

In this talk, I will demonstrate the higher order linearization approach to solve several inverse boundary value problems for nonlinear PDEs modeling nonlinear electromagnetic optics including nonlinear time-harmonic Maxwell’s equations with Kerr...

Any translation surface can be presented as a collection of polygons in the plane with sides identified. By acting linearly on the polygons, we obtain an action of GL(2,R) on moduli spaces of translation surfaces. Recent work of Eskin, Mirzakhani...

Diffusion methods help understand and denoise data sets; when there is additional structure (as is often the case), one can use (and get additional benefit from) a fiber bundle model.

The Monge transfer problem goes back to the 18th century. It consists in minimizing the transport cost of a material from a place to another (and changing the shape). Monge could not solve the problem and the next significant step was achieved 150...