We discuss the existence problem of constant Chern scalar
curvature metrics on a compact complex manifold. We prove a priori
estimates for these metrics conditional on an upper bound on the
entropy, extending a recent result by Chen-Cheng in the...
I shall present two billiard-like systems associated with
a convex hypersurface in a symplectic space, the outer and an
inner ones. The talk will survey the known results and
focus on open problems.
Let K be a knot or link in the 3-sphere, thought of as the ideal
boundary of hyperbolic 4-space, H4. The main theme of my talk is
that it should be possible to count minimal surfaces in H4 which
fill K and obtain a link invariant. In other words...
In this three-part lecture series, we will present a series of
works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic
mixing and enhanced dissipation properties of a passive tracer
subject to the motion of an ergodic Markovian flow of...
Half-integral weight modular forms are classical objects with
many important arithmetic applications. In terms of
automorphic representations, these correspond to objects on the
metaplectic double cover of SL(2). In this talk, I will
outline a...
I will present a recent result jointly with Francisco Gancedo
(Universidad de Sevilla) and Huy Q. Nguyen (University of
Maryland), in which we obtained the global well-posedness for the
2D one-phase Muskat problem with arbitrary large Lipschitz...
I will discuss an idea of constructing a category associated
with a pair of holomorphic Lagrangians in a hyperkahler manifold,
or, more generally, a manifold equipped with a triple of almost
complex structures I,J,K satisfying the quaternionic...
The Hochschild cohomology of the Floer algebra of a Lagrangian
L, and the associated closed-open string map, play an important
role in the generation criterion for the Fukaya category and in
deformation theory approaches to mirror symmetry. I will...
In this three-part lecture series, we will present a series of
works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic
mixing and enhanced dissipation properties of a passive tracer
subject to the motion of an ergodic Markovian flow of...