School of Mathematics

The Hopf-Tsuji-Sullivan theorem states that the geodesic flow on (an infinite) Riemann surface is ergodic iff the Poincare series is divergent iff the Brownian motion is recurrent. Infinite Riemann surfaces can be built by gluing infinitely many...

Complex lines are a class of pseudoholomorphic curves which generalize rational curves. Applications of complex lines to symplectic geometry have been proposed, but they remain poorly understood. In this talk, I will describe a framework for...

Given linear equations over a finite field and under infinity norm, the Short-Integer-Solution (SIS^inf) problem asks to find a solution where each entry is a small number.

In 2021, Chen, Liu, and Zhandry presented an efficient quantum algorithm for...

By an observation of Efimov and Scholze, Efimov's theorem on the rigidity of localizing motives allows one to construct refinements of topological Hochschild homology and its variants. In this talk, I'll explain how this refinement works, sketch an...

The SAT (Boolean Satisfiability) problem asks whether a given logical formula on n Boolean variables has an assignment of true/false values to its variables that makes the formula true.  The P vs NP question is equivalent to asking whether SAT has a...

Matrix-perturbation bounds quantify how the spectral characteristics of a baseline matrix A change under additive noise E. Classical results, including Weyl’s inequality for eigenvalues and the Davis–Kahan theorem for eigenvectors and eigenspaces...

In this talk I will introduce a new notion of approximability for metric spaces that can be seen as a categorification of a concept introduced by Turing for metric groups and as a generalization of total-boundedness. I will explain how recent...

Rational curves are one of the main tools in symplectic geometry and provide a bridge to algebraic geometry. Complex lines are a more general class of curve that has the potential to connect symplectic and complex analytic geometry. These curves are...

Link spectral invariants and their homogenizations have been defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim Trifa, we define a linear combination of such quasimorphism and show that it vanishes on the stabilizer of the equator in...

In this talk, I will discuss some effective computations for variations of integral Hodge structures.

Several years ago, with Ren and Javanpeykar-Kühne, I conjectured (in the Shimura setting) that a variation has only finitely many "non-factor"...