Title: Shtukas and their cohomology. Abstract: I will introduce the moduli space of shtukas and explain a spectral description of their cohomology using categorical traces along a Frobenius endomorphism. Reference: https://arxiv.org/abs/1606.09608
We will be having a a mixer with the undergrad physics club SPS on Friday in Bloomberg 462 at 430pm. We will have jeopardy, lots of nice free food, an integration bee, and other fun activities planned! Come by for a fun time!
Title: Triple junction solution for the Allen-Cahn systemAbstract: In this talk, I will discuss recent results on the vector-valued Allen-Cahn system with a triple-well potential. We establish the existence of an entire minimizing solution that asymptotically converges to a triple junction, corresponding to a planar minimal cone, at infinity. Furthermore, we prove the uniqueness of […]
Title: Hodge symmetries of singular varieties.Abstract: The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge–Du Bois diamond. For example, the failure […]
Title: Higher Modularity of Elliptic Curves Abstract: Elliptic curves E over the rational numbers are modular: this means there is a nonconstant map from a modular curve to E. When instead the coefficients of E belong to a function field, it still makes sense to talk about the modularity of E (and this is known), […]
Title - Variations of the Yang-Mills Lagrangian in high dimensionAbstract - In this talk we will present some analysis aspects of gauge theory in high dimension. First, we will study the completion of the space of arbitrary smooth bundles and connections under L^2-control of their curvature. We will start from the classical theory in critical […]
Title: Relative Langlands duality. Abstract: We will review those aspects of the conjectures of Ben-Zvi–Sakellaridis–Venkatesh, that are relevant to the preprint https://arxiv.org/abs/2504.00275 by Liu and Wang. Reference: https://arxiv.org/abs/2409.04677.
Title: Stable maps to quotient stacks with a properly stable point.Abstract: I will present a compactification of the moduli space of maps from families of curves, to certain moduli spaces M, via the example of M being the GIT moduli space of binary forms of degree 2n. The main application of our results is the construction of […]