Interior Hessian estimates for singularities of the Lagrangian mean curvature flow Abstract. In this talk, we discuss the history of the Lagrangian Mean Curvature equation beginning with the special Lagrangian equation of Harvey and Lawson. We consider the hypercritical case … Read more
Semi-infinite flag manifolds, space of maps, and quantum K-groups of flag manifolds Abstract: We first recall the Plucker relations, that yield a description of a(n open) space of maps from a projective line to a (partial) flag manifolds. Then, we … Read more
Gravity water waves with constant vorticity at low regularity and balanced energy estimates Abstract. In this talk I will talk about the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive … Read more
Algebraic models of semi-infinite flag manifolds Abstract. We first recall the classical Borel-Weil-Bott theorem and examine its representation-theoretic meaning. Then, we exhibit affine analogue of their representation-theoretic meaning and form several schemes. Finally, we identify the resulting schemes with so-called … Read more
On the Donaldson-Scaduto conjecture. Abstract. Donaldson proposed a new method to study manifolds with special holonomy groups, particularly Calabi-Yau 3-folds and G2-manifolds, utilizing a Lefschetz fibration. Motivated by collapsing G2-manifolds with K3 fibrations in the adiabatic setting, Donaldson and Scaduto … Read more
Mixed norm decoupling for paraboloids Abstract. In this talk we discuss mixed norm decoupling estimates for the paraboloid. One motivation for considering such an estimate is a conjectured mixed norm Strichartz estimate on the torus. This is joint work with … Read more
Cellular pavings of convolution fibers and applications Abstract. A convolution morphism is the geometric analogue of a convolution of functions in a Hecke algebra. The properties of fibers of convolution morphisms are used in a variety of ways in the … Read more
Recovery of time-dependent coefficients in hyperbolic equations on Riemannian manifolds from partial data. Abstract. In this talk we discuss inverse problems of determining time-dependent coefficients appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. … Read more
On the Poisson summation conjecture Abstract: Braverman, Kazhdan, Lafforgue, Ngo, and Sakellaridis have conjectured that Fourier analysis on a vector space is but the first example of a larger phenomenon. More generally, one should have Schwartz spaces, Fourier transforms, and, … Read more
On the global well-posedness of the Boltzmann hierarchy Abstract. The Boltzmann hierarchy is an infinite system of linear coupled equations that are instrumental for the rigorous derivation of the Boltzmann equation from many particles. In this talk we will show … Read more
Row-Column Mirror Symmetry for Colored Torus Knot Homology Abstract. The HOMFLYPT polynomial is a 2-variable link invariant generalizing the celebrated Jones polynomial and other Type A quantum link polynomials. Its construction passes through a Hecke algebra representation of the braid … Read more
Eigenvalue Optimization and Minimal Surfaces Abstract. I will discuss a new method, developed in collaboration with M. Karpukhin, R. Kusner, and D. Stern, for constructing minimal surfaces embedded in the 3-sphere and the 3-ball, by equivariant eigenvalue optimization. A main … Read more
