Video Lectures

For a compact Lie group G and a Hamiltonian G-space M, can we find a smooth weak deformation retraction from a neighbourhood of the zero level set of the momentum map onto it? If we do not require smoothness then this is already known, in fact one...

The symplectic squeezings in the cotangent bundle of a torus is distinct from those in $R^{2n}$, due to the nontrivial topology of the torus. In this talk, we will show that for $n\ge2$ any bounded domain of $T^*T^n$ can be symplectically embedded...

We introduce an equivariant Lagrangian Floer theory on compact symplectic toric manifolds. We define a spectral sequence to compute the equivariant Floer cohomology. We show that the set of pairs $(L,b)$, each consisting of a Lagrangian torus fiber...

The LIGO-Virgo-KAGRA detector network has observed over 70 gravitational-wave sources to date, including mergers between black holes, neutron stars, and mixed neutron star-black holes. Focusing on the black hole mergers, I will describe some recent...

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...