Talks

In this talk, I will describe some work in progress about relating the low-lying spectrum of the Davies Lindbladian for qLDPC codes to that of Glauber dynamics on a classical model.

I will describe the new approach to scattering theory, which extends to time dependent potentials, including nonlinear equations. In particular, recent progress for one dimensional cases, Long-Range scattering and Local-Decay estimates.

For Schrödinger-type equations with time-dependent, spatially local interactions — including nonlinear cases — there exist solutions that are neither localized nor scattering. These solutions exhibit sub-ballistic spreading, yet are global, asymptotically stable, and transport mass (the L^2-norm) to infinity. I will describe the construction of such self-similar solutions and discuss some of their physical implications.

We consider stochastic growth models in the Kardar-Parisi-Zhang universality class, like the asymmetric simple exclusion process or the last passage percolation. We will give an overview of older and recent results on the limit process and its properties for KPZ growth models with flat initial conditions, ranging from regularity, decorrelation in space and time, to […]

Under suitable assumptions, a Markov chain will converge at large times to its stationary measure, over a time scale known as the mixing time. Markov chains can then be used to approximately sample from a complex distribution, which is the principle underlying Markov Chain Monte Carlo techniques. In this context, there has been strong interest […]

The standard approach to studying the liquid-vapor phase transition uses the Maxwell double-tangent construction. Whereas this construction is easily justified physically, deriving it mathematically has proved to be more difficult. In 1966, Lebowitz and Penrose proved the Maxwell construction in a mean field model, where the particles interact via a hard-core repulsion, and an infinite […]

The study of the electronic properties of twisted bilayer graphene (TBG) has garnered much attention from the condensed matter community recently. TBG is obtained by stacking two graphene monolayers on top of each other, and rotating one of them with respect to the other. Theoretical and experimental analyses have found that the electronic properties of […]