Talks

We will discuss some aspects of my recent preprint, joint with Victor Ginzburg, on Kostant-Whittaker reduction, a (deformation) quantization of restriction to a Kostant slice. We will explain how this functor can be used to prove conjectures of Ben-Zvi and Gunningham on parabolic induction, as well as a convolution exactness conjecture of Braverman and Kazhdan in the D-module setting. While this talk will occasionally reference facts from a talk I gave at Perimeter on other aspects of this preprint, the overlap and references will be minimal.

Over the past two decades our understanding of the charge and heat transport properties of graphene has evolved progressively as the quality of the graphene devices improved. A key crossover occurs when the scattering between electrons themselves become more frequent than the scattering between electrons and disorder. In this regime, the electrons gas behaves as a hydrodynamic fluid, whose properties exhibit emergent universalities close to the charge neutrality point. In this talk, I shall present some new experimental result on the electrical and thermal transport measurements in very high-quality graphene devices where electron-electron scattering dominates over the momentum relaxation rate. I shall show that the transport in such graphene devices is unique in multiple ways, ranging from unconventional functional dependence of the dc conductivity on carrier density to giant violation of the Wiedemann-Franz law, where effective Lorenz number varies over six orders of magnitude with carrier density. We find that the transport properties of ultra-clean graphene close to charge neutrality are quantitatively consistent with that of a hydrodynamic Dirac fluid where both charge and heart flow are determined by a single universal transport constant.
 

Common intuition tells us that if one part of an interacting system is continuously cooled, the other parts should also cool down. This intuition can be put on firm grounds for the case of Markovian cooling of a free-fermion "lead" that is locally coupled to a generic quantum system. I will talk about a scenario where the opposite happens, namely, the system heats up toward its most excited state as the lead is cooled (or vice versa), even if other parameters favor sympathetic cooling. This dramatic effect originates from a simple but structured coupling that preserves a U(1) charge, and is realizable as existing setups.

Quantum steering is a protocol made up of successive measurements of the system, employing the back-action generated to push the system towards a desired target state. The latter may be the ground state of the system’s Hamiltonian, thus cooling the system to “zero temperature”. I will address here two questions: (1) Can we achieve such cooling by acting only on a small section of the system (a protocol we denote “dilute cooling”)? (2) When such cooling to zero
temperature is not feasible - how low in temperature can we go?
 

Interannual variability in Asian Summer Monsoon rainfall features two modes that are correlated with concurrent and preceding winter ENSO, respectively. The latter post-ENSO effect is especially puzzling. The lecture explains how coupled ocean-atmospheric modes affect the Asian Summer Monsoon.

The string-net model introduced by M. Levin and X.-G. Wen in 2005 allows one to generate all (bosonic) topological  achiral phases in two dimensions. In this talk, I will explain how to compute the exact partition function of this model and discuss the finite-temperature properties of several quantities such as the topological mutual information. These results show that, in this context, topological order can only survive up to a temperature which depends on the system size and goes to zero in the thermodynamical limit.

We consider a gas of non-interacting fermions that is released from a box into the vacuum. This provides a simple analytically tractable model that reproduces many features of the Page curve characterizing the evolution of entanglement entropy during evaporation of a black hole. Apart from the entropy we consider several other physical observables and show that generalized hydrodynamics provides a rather surprisingly accurate description of the quantum dynamics.
 

The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be simplified by a formulation in terms of the appropriate dynamical degrees of freedom.