Title: Skein theory and the geometric Langlands program.Abstract: Skein modules are certain families of vector spaces spanned by embedded links or graphs in a 3-manifold M, modulo certain local relations. They can be thought of both as an obstruction to defining a polynomial invariant of knots in M and as an invariant of the 3-manifold […]
Title: On the existence of isoperimetric sets on nonnegatively curved spaces Abstract: In this presentation, I will deal with the isoperimetric properties of spaces with nonnegative curvature, placing special emphasis on the existence of isoperimetric sets in the non-compact case. Isoperimetric sets of any volume do exist in compact Riemannian manifolds. Conversely, it is possible to construct simple examples […]
Title: On Fano and Calabi-Yau pairs of small coregularity.Abstract: The coregularity is an invariant that measures a specific type of combinatorial complexity of a pair. We will start this talk by defining this invariant and giving some examples. Then, we will explain how results about complements of Fano varieties of bounded dimension are still valid for Fano […]
Title: Degenerate, Generalized, and Reduced Whittaker models Abstract: Whittaker models are realizations of representations on a space of functions that transform in a certain way under the action of a unipotent group, and they have been central in both the local representation theory and the global theory of automorphic representations. For groups other than GL_n, […]
Title: Coherence theorems in the style of Mac LaneAbstract: The aim is to discuss different equational structures defined on categories like monoidal, symmetric monoidal and cartesian monoidal structures. The aim is to shed light on the associated coherence theorems and to show how these are related to the construction of simple type theories. This suggests a more general approach […]
Title: Stability for Vlasov and Hartree equations Abstract: I focus on presenting the survival threshold of wave numbers found in mean field equations such as Vlasov and Hartree equations, which completely characterizes the large time behavior of linearized equations near non-trivial backgrounds into plasma oscillations, Landau damping, and phase mixing regime. I shall also mention progress […]
Title: Speculations on Computations with the Relative Trace Formula. Abstract: This is a continuation of the talk from 9/15. I will discuss how many statistics of automorphic representations have been computed previously using "explicit" forms of Arthur's trace formula. I will then present a very speculative plan to develop similar "explicit" versions of relative trace […]
Title: Kapustin-Witten (KW) and Kapustin-Rozanksy-Witten (KRS) theory path to knot homologyAbstract: My talk is based on the joint project with Lev Rozansky. As a motivation, I will interpret KRS theory as KW theory with defects. Then I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of […]
Title: Why you should take Differential EquationsAbstract: A first encounter with differential equations often leaves the impression that differential equation is just integrating with extra steps. In this talk we'll show that what it means to "solve" a differential equation is more subtle (and mathematically interesting) than it initially appears. We'll also describe how these different types of "solutions" contribute to the […]
Title: Minimal model program for algebraically integrable foliations and generalized pairs.Abstract: In this talk, I will discuss my recent research that establishes the minimal model program for Q-factorial foliated dlt algebraically integrable foliations and log canonical generalized pairs. This is joint work with G. Chen, J. Han, and L. Xie.
Title: Root Number Correlation Bias of Fourier Coefficients of Modular FormsAbstract: In a recent machine learning based study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the P-th Frobenius trace of elliptic curves of prescribed rank and conductor in an interval range. Sutherland discovered that this bias extends to […]
Title: Well-Posedness of the 3D Peskin ProblemAbstract: This work introduces the 3D Peskin problem: a two-dimensional elastic membrane immersed in a three-dimensional steady Stokes flow. We obtain the equations that model this free boundary problem and we show that these equations admit a boundary integral reduction. This provides an evolution equation for the elastic interface. We also […]