Department of Mathematics

Title: Free fermions and the equivariant string orientation at the Tate curveAbstract: I will describe recent work (joint with Kiran Luecke and Langwen Hui) that constructs a geometric model for the (twisted) equivariant string orientation at the Tate curve. The primary ingredients come from loop group representation theory and the Stolz-Teichner program. As a warm-up […]

Title: Multivariate V-filtration and Strong Monodromy Conjecture for hyperplane arrangementsAbstract: In singularity theory, the Strong Monodromy Conjecture is a long-standing open problem predicting a deep connection between the poles of the p-adic, topological, and motivic zeta functions of a polynomial and the roots of its Bernstein-Sato polynomial. To date, this conjecture has only been verified in low […]

Title: On Breuil's Lattice Conjecture for GL_2 Abstract: Let $K$ be an extension of $Q_p$ and $E$ be a finite extension of $Q_p$ which is sufficiently large. We seek a -adic Langlands correspondence between a Galois representation $rho: Gal (overline{K}/K) to GL_2(E)$  and an admissible unitary Banach space representation of $GL_2(K)$ over $E$. This correspondence is […]

Title: Solving the constraint equation for general free data Abstract: We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that once appropriate gauge conditions have been chosen […]

Title: Learning Pseudo-Differential OperatorsAbstract: Pseudo-differential operators (PDOs) are a broad and fundamental class of operators in partial differential equations and mathematical physics. In this talk I will present recent work with Jiaheng Chen on learning elliptic PDOs from noisy data. Within a wavelet--Galerkin framework, we formulate this task as a structured infinite-dimensional regression problem with […]

Title: Moduli spaces of expanding Ricci solitons asymptotic to conesAbstract: Expanding Ricci solitons are a kind of self-similar solution of the Ricci flow.  Asymptotically conical (AC) examples are interesting because they can be used to resolve conical singularities of 4D Ricci flow.  I will describe a moduli space structure on spaces of AC expanding Ricci […]