It is well-known that a random walk on a (connected, finite, non-bipartite) graph converges to its invariant distribution. For some graphs it has been observed that this convergence happens rather abruptly. This phenomenon is called cutoff, and it has been established widely, but in general there is little understanding for what causes it.

In this work we consider a model with a small amount of randomness. Given some deterministic graphs, we apply a random perturbation on them and based on the strength of the perturbation, we establish a phase transition in whether the resulting graphs have cutoff.

The first part of the talk will be an overview about mixing times and cutoff. In the second part we will focus on our model and explain the ideas behind the results.

Based on joint work with Jonathan Hermon, Andela Sarkovic and Perla Sousi.

In recent years we've greatly expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. While entanglement is very difficult to measure in experiments, it has nevertheless driven progress in 1) the classification of quantum phases of matter and 2) strategies for efficiently simulating many-body systems on classical and quantum computers. I will review some recent progress in these directions. Along the way I will summarise some older results on how entanglement grows in many-body systems, briefly highlight some connections to holography, and present a conjecture about the asymptotic computational difficulty of calculating transport in many-body systems.

Quantum chaotic systems display correlation between eigenvalues as described by the random matrix theory (RMT). I will present three results on the universal aspects of many-body quantum chaos that go beyond the standard RMT paradigm. Firstly, I will present an exact scaling form of the spectral form factor (SFF) in a generic many-body quantum chaotic system, deriving the so-called "bump-ramp-plateau" behaviour. Secondly, I will introduce and provide an analytical solution of a generalization of SFF for non-Hermitian matrices, called Dissipative SFF, which displays a "ramp-plateau" behaviour with a quadratic ramp. Thirdly, I will provide evidences that non-Hermitian Ginibre ensemble behaviour surprisingly emerge in generic many-body quantum chaotic systems, due to the presence of many-body interaction.

For a compact Lie group G, its massless Coulomb branch algebra is the G-equivariant Borel-Moore homology of its based loop space. This algebra is the same as the algebra of regular functions on the BFM space. In this talk, we will explain how this algebra acts on the equivariant symplectic cohomology of Hamiltonian G-manifolds when the symplectic manifolds are open and convex. This is a generalization of the closed case where symplectic cohomology is replaced with quantum cohomology. Following Teleman, we also explain how it relates to the Coulomb branch algebra of cotangent-type representations. This is joint work with Eduardo Gonz��lez and Dan Pomerleano.

After a PhD in cosmology, Vincent co-founded B12 Consulting with two other physicists. This company specializes in developing custom AI solutions, tailored for various business and organizational needs. The team now comprises over 40 individuals, primarily from science backgrounds including mathematics, physics, and engineering, with half holding PhDs. This diverse expertise fuels innovative approaches and solutions in their projects. In this presentation, Vincent will discuss his personal journey to becoming an entrepreneur, focusing on the challenges of bridging academic research with the world of business.

https://www.b12-consulting.com/en/team/vincent-boucher/

We propose a new method for changepoint estimation in partially-observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a 'MissCUSUM' transformation (a generalisation of the popular Cumulative Sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the coordinates, we propose to project these MissCUSUM statistics along a direction found as the solution to a penalised optimisation problem tailored to the specific sparsity structure. The changepoint can then be estimated as the location of the peak of the absolute value of the projected univariate series. In a model that allows different missingness probabilities in different component series, we identify that the key interaction between the missingness and the signal is a weighted sum of squares of the signal change in each coordinate, with weights given by the observation probabilities. More specifically, we prove that the angle between the estimated and oracle projection directions, as well as the changepoint location error, are controlled with high probability by the sum of two terms, both involving this weighted sum of squares, and representing the error incurred due to noise and the error due to missingness respectively. A lower bound confirms that our changepoint estimator, which we call 'MissInspect', is optimal up to a logarithmic factor. The striking effectiveness of the MissInspect methodology is further demonstrated both on simulated data, and on an oceanographic data set covering the Neogene period.

Many important examples of Banach algebras are also dual Banach spaces, and over the last thirty years a theory of so-called dual Banach algebras has emerged. An interesting and important way to study a dual Banach algebra is by studying (or even classifying) its weak*-closed (left/right/two-sided) ideals. It also turns out that weak*-closed ideals have connections to other topics as well, such as asymptotic properties of group representations.

In this talk we shall give an introduction to this topic, with our main examples being the measure algebra M(G) of a locally compact group G, and algebras of convolution operators on l^p spaces. We shall describe classifications of the weak*-closed (left/right/two-sided) ideals in M(G) for certain classes of groups G. Finally, we shall outline some new results about weak*-simplicity of M(G) and algebras of convolution operators.