School of Mathematics

Projection theory asks how the size of a set in Rn—often measured by Hausdorff dimension—behaves under projections onto lower-dimensional spaces, both for orthogonal projections and for more general nonlinear families. One would like to understand...

Projection theory asks how the size of a set in Rn—often measured by Hausdorff dimension—behaves under projections onto lower-dimensional spaces, both for orthogonal projections and for more general nonlinear families. One would like to understand...

Note: This talk will involve quantum computing, cryptography, and representation theory, but no background in any of these will be necessary to understand it. I'll introduce everything from the basics.

Aaronson, Atia, and Susskind (2020) established...

Let C be a closed surface and Σ⊂T*C a real exact Lagrangian surface associated to a spectral curve. In this talk we will first try to explain the context of this work (e.g., Higgs bundles and spectral curves). We then construct a homomorphism from...

Jacobi's theta function Θ(q):=1+2q+2q4+2q9+…, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely...

The Pila–Zannier strategy has proved to be a particularly fruitful approach: first applied to reprove the Manin–Mumford conjecture, it was later exploited decisively in proofs of the André–Oort conjecture. Crucially relying on a recent counting...

Rank 1 transformations are a long studied, flexible class of measure preserving transformations. King proved a variety of deep results about rank 1 rank transformations including: A) A rank 1 transformation’s centralizer is the weak closure of its...

In the '80s, Yau conjectured that every closed Riemannian 3-manifold contains infinitely many smooth minimal hypersurfaces. In this talk, I will present a Yau-type existence result for nonlocal minimal surfaces and discuss how one can recover the...

A closed hypersurface in a contact manifold is convex if it admits a transverse contact vector field. A closed hypersurface is robustly non-convex if it cannot be smoothly approximated by a convex hypersurface. The existence of such hypersurfaces...

I plan to survey the many ways we have today of constructing expanding Cayley graphs of finite groups, and the ideas behind their analysis (some useful beyond that purpose). I want to highlight that despite a comprehensive understanding of achieving...