The unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of SL_2(Z) whose Fourier coefficients have bounded denominators must be...
Read more
Language models typically need to be trained or fine-tuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and...
Read more
We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information-theoretic formulation of the exact renormalization group,...
Read more
We present an effective quantization theory for chiral deformation of two dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex...
Read more
We present an effective quantization theory for chiral deformation of two dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex...
Read more
I will discuss the asymptotics of multimatrix models. In a small parameters (or high temperature) region, their free energy is well known to converge and to be related with the...
Read more
How often does a general cubic surface appear in a 4-dimensional linear system? As a slice of a general cubic 3-fold? I will describe how we can solve problems of...
Read more
I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black...
Read more
I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of...
Read more
I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk...
Read more