Video Lectures

Topological Hochschild homology is an important invariant, closely related to algebraic K-theory, and can be seen as a noncommutative analogue of de Rham chains.

In this talk, I will describe various computations of the ring/monoid of endomorphisms...

The Fourier uniformity conjecture seeks to understand what multiplicative functions can have large Fourier coefficients on many short intervals. We will discuss recent progress on this problem and explain its connection with the distribution of...

For the past 25 years, a key player in contact topology has been the Floer-theoretic invariant called Legendrian contact homology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and...

For nearly a decade, beginning in the mid-1970s, a debate unfolded among physicists and engineers over how best to include effects from Einstein's general theory of relativity in the new military technology now known as the Global Positioning System...

Around twenty years ago Emmanuel Giroux formulated the equivalence of contact structures and open book decompositions with Weinstein pages up to stabilization. We establish the Giroux correspondence in full generality using the recent developments...

In the original CPT theorem one is restricted to flat space and is unable to make converse statements. In this talk I will show how we can reformulate the CPT theorem using a symmetry argument and generalise it to beyond flat space. This in turn...

The Milky Way contains of order 10^8 stellar-mass black holes (BHs). Yet, fewer than 100 BH candidates are known, and only about 20 are dynamically confirmed. Our view of the BH population has been shaped almost entirely by observations of X-ray...

Let π be a cuspidal automorphic representation of Sp_2n over Q which is holomorphic discrete series at infinity, and χ a Dirichlet character. Then one can attach to π an orthogonal p-adic Galois representation ρ of dimension 2n+1. Assume ρ is...

Endow the edges of the ZD lattice with positive weights, sampled independently from a suitable distribution (e.g., uniformly distributed on [a,b] for some b greater than a greater than 0). We wish to study the geometric properties of the resulting...