Mode: In-person Title: Birational geometry of Beauville-Mukai systems on K3 surfaces Abstract: A Beauville-Mukai system on a K3 surface is a moduli space of stable torsion sheaves, which admits a Lagrangian fibration given by mapping each sheaf to its support. … Read more
Mode: In-person Title: Counting closed geodesics and improving Weyl’s law for predominant sets of metrics Abstract: We discuss the typical behavior of two important quantities on compact manifolds with a Riemannian metric g: the number, c(T, g), of primitive closed … Read more
Mode: In-person Title: Quantitative unique continuation for L 2 -restrictions of eigenfunction sequences Abstract: Let (M, g) be a C ∞ compact, Riemannian manifold and uh ∈ C ∞(M) be a sequence of L 2 -normalized Laplace eigenfunctions with (−h … Read more
Mode: In-person Title: Geometric variational problems: regularity vs singularity formation Abstract: I will describe in a very informal way some techniques to deal with the existence ( and more qualitatively regularity vs singularity formation) in different geometric problems and their … Read more
Mode: In-person Title: The P=W conjecture for GL_n Abstract: In 2010, de Cataldo-Hausel-Migliorini proposed a conjecture connecting topology of the Hitchin system and Hodge theory of the corresponding character variety via the non-abelian Hodge theory. This conjecture is now referred … Read more
Mode: Zoom Title: Spatial-Temporal Differentiation Theorems Abstract: We present a type of ergodic-theoretic differentiation problem that synthesizes spatial and temporal differentiation problems, creatively termed a spatial-temporal differentiation problem. We describe the problem, and present various convergence results. Based on joint … Read more
Mode: In-person Title: Numerical Approaches for Computing Quasi-stationary Distributions Abstract: Markov processes with absorbing states occur frequently in epidemiology, statistical physics, population biology, and other areas. Quasi-stationary distributions (QSD) are the basic mathematical object used to describe the long-time behavior … Read more
Mode: In-person Title: A determination of the blowup solutions to the focusing, quintic NLS with mass equal to the mass of the soliton Abstract: In this talk we prove that the only blowup solutions to the focusing, quintic nonlinear Schrodinger … Read more
Mode: In-Person Title: Signature, Toledo invariant, and the surface group representations in Hermitian semisimple Lie groups Abstract: People study higher Teichmuller theory and using several invariants, one tries to characterize the representations. We give a unifying formula between (Atiyah-Patodi-Singer) signature, … Read more
Mode: In person Title: Opers and Integrable Systems Abstract: I will explain how the geometric construction of opers (as well as its difference and elliptic generalizations) is related to quantum and classical integrable systems. Opers thereby provide a framework to … Read more
