Past Events
Abstract: Symmetric products of Riemann surfaces play a crucial role in symplectic geometry and low-dimensional topology. They are key to defining Heegaard Floer homology and serve as important examples of Liouville manifolds when the surfaces are open. In this talk, I will present ongoing work…
We present a new structure on the first Galois cohomology of families of symplectic self-dual p-adic representations of $G_Qp$ of rank two. This is a functorial decomposition into free rank one Lagrangian submodules encoding Bloch-Kato subgroups and epsilon factors, mirroring an underlying…
We will continue our study of the lace expansion and its applications.
The special Lagrangian equation (SLE) is a fully nonlinear elliptic PDE that originates in the work of Harvey and Lawson on calibrated geometries. The question whether a viscosity solution to the SLE is smooth (or at least has minimal gradient graph) is delicate, and the answer depends on the…
Let Q be a non-degenerate indefinite quadratic form with at least 3 variables. In the 1980s Margulis proved the longstanding Oppenheim Conjecture, stating that unless Q is proportional to an integral form, the set of values Q attaining at the integer points is dense in R. In Margulis' seminal…
We will ponder the following question: Suppose we have a finite group of order between n and 2n. How large of an abelian subgroup must it have? This question will lead us to some strange proofs and wild constructions, and to another fairly natural group theory problem…
In the past two decades, the field of topological data analysis (TDA) has significantly advanced scientific research and raised new mathematical inquiries. Nonetheless, key challenges in statistical methodology and domain-specific interpretations persist. In this talk, I will discuss my…
Critical holomorphic multiplicative chaos (HMC) arises naturally from the studies of characteristic functions of CUE and partial sums of random multiplicative functions. We investigate the low moments of secular (Fourier) coefficients of the critical HMC. We establish:
- universality…