Talks

We study the infrared on-shell action of Einstein gravity in asymptotically flat spacetimes, obtaining an effective, gauge-invariant boundary action for memory and shockwave spacetimes. We show that the phase space is in both cases parameterized by the leading soft variables in asymptotically flat spacetimes, thereby obtaining an equivalence between shockwave and soft commutators. We then demonstrate that our on-shell action is equal to three quantities studied separately in the literature: (i) the soft supertranslation charge; (ii) the shockwave effective action; and (iii) the soft effective action.

Scientists are always working on the forefront of technology, developing new ideas and solving important problems. But many researchers don’t realize that their work can be protected—and potentially monetized for a profit!—by filing a patent application. In this presentation, we will talk about the types of inventions that can be patented, and the benefits of getting a patent for your invention. We will also discuss practical aspects of the patent process, and how you can best prepare yourself for success.

We say that an ordinary or partial differential equation is regularized by noise if the addition of a suitable noise term restores well-posedness or improves regularity of the solution to the equation. Regularization by noise is by now well understood for ODEs and linear transport-type PDEs, but it is less understood for nonlinear PDEs like Euler and Navier-Stokes equations, with many open questions.

In the first part of this series of lectures, we consider the case of ODEs and associated transport equations with irregular drift: we show that the addition of an additive Brownian noise restores well-posedness of the ODE; we introduce the corresponding transport noise and show that this noise restores well-posedness for the associated transport equation. In the second part, we focus our attention on the effect of a particular transport-type noise, which is divergence-free, Gaussian, white in time and poorly correlated in space (nonsmooth Kraichnan noise). The associated linear transpo...

In 1949 Onsager conjectured the existence of Hoelder continuous solutions of the incompressible Euler equations which do not conserve the kinetic energy. A rigorous proof of his statement has been given by Isett in 2017, crowning a decade of efforts in the subject. Onsager's original statement is however motivated by anomalous dissipation in the Navier-Stokes equations: roughly speaking it would be desirable to show that at least some dissipative Euler flow is the ``vanishing viscosity limit''. In these lectures I will review the basic ideas of the first iteration invented by La'szlo' Sze'kelyhidi Jr. and myself to produce continuous solutions which dissipate the total kinetic energy. I will then review the developments which lead Isett to solve the Onsager conjecture and touch upon the new challenges which lie ahead. 

There is a well-known discrepancy in mathematical fluid mechanics between phenomena that we can observe and phenomena on which we have theorems. The challenge for the mathematician is then to formulate an existence theory of solutions to the equations of hydrodynamics which is able to reflect observation. The most important such observation, forming the backbone of turbulence theory, is anomalous dissipation. In the talk, we survey some of the recent developments concerning weak solutions in this context.

In the recent resolution of the strong Onsager’s conjecture in L^3 framework, so-called wavelet-inspired Nash’s iteration has been developed. In this lecture, we will sketch this new method and provide the necessary background. The lecture will be based on our recent joint work with Matthew Novack.

We say that an ordinary or partial differential equation is regularized by noise if the addition of a suitable noise term restores well-posedness or improves regularity of the solution to the equation. Regularization by noise is by now well understood for ODEs and linear transport-type PDEs, but it is less understood for nonlinear PDEs like Euler and Navier-Stokes equations, with many open questions.

In the first part of this series of lectures, we consider the case of ODEs and associated transport equations with irregular drift: we show that the addition of an additive Brownian noise restores well-posedness of the ODE; we introduce the corresponding transport noise and show that this noise restores well-posedness for the associated transport equation. In the second part, we focus our attention on the effect of a particular transport-type noise, which is divergence-free, Gaussian, white in time and poorly correlated in space (nonsmooth Kraichnan noise). The associated linear transpo...

There is a well-known discrepancy in mathematical fluid mechanics between phenomena that we can observe and phenomena on which we have theorems. The challenge for the mathematician is then to formulate an existence theory of solutions to the equations of hydrodynamics which is able to reflect observation. The most important such observation, forming the backbone of turbulence theory, is anomalous dissipation. In the talk, we survey some of the recent developments concerning weak solutions in this context.

A computational phase transition in a classical or quantum system is a non-analytic change in behavior of an order parameter which can only be observed with the assistance of a nontrivial classical computation. Such phase transitions, and the computational observables which detect them, play a crucial role in the optimal decoding of quantum error-correcting codes and in the scalable detection of measurement-induced phenomena. We show that computational phase transitions and observables can also provide important physical insight on the phase diagram of a classical statistical physics system, specifically in the context of the dislocation-mediated melting of a two-dimensional antiferromagnetic (AF) crystal. In the solid phase, elementary dislocations disrupt the bipartiteness of the underlying square lattice, and as a result, pairs of dislocations are linearly confined by string-like AF domain walls. It has previously been argued that a novel AF tetratic phase can arise when double dislocations proliferate while elementary dislocations remain bound. We will argue that, although there is no thermodynamic phase transition separating the AF and paramagnetic (PM) tetratic phases, it is possible to algorithmically construct a nonlocal order parameter which distinguishes the AF and PM tetratic regimes and undergoes a continuous computational phase transition. We discuss both algorithm-dependent and "intrinsic" algorithm-independent computational phase transitions in this setting, the latter of which includes a transition in one's ability to consistently sort atoms into two sublattices to construct a well-defined staggered magnetization.