Title: Transfer operators over finite fields Abstract: I will explain some analogies between the local Langlands correspondence and Lusztig’s classification, and the resulting analogue of transfer operators.
Title: Directed univalence and the Yoneda embedding for synthetic (∞,1)-categoriesAbstract: I'll present recent advances in synthetic (∞,1)-category theory, more specifically a modal extension of Riehl--Shulman's simplicial homotopy type theory. This includes […]
Title: Towards a birational geometric version of the monodromy conjecture.Abstract: The monodromy conjecture of Denef—Loeser is a conjecture in singularity theory that predicts that given a complex polynomial f, and any pole […]
Title: Surfaces and Differential GeometryAbstract: Informally, differential geometry is using calculus to study smooth objects. More formally, it is the study of smooth objects that locally look like R^n. Classically, differential […]
Title: Kakeya sets in R^3 Abstract: A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction. Kakeya set conjecture asserts that […]
Title: Poisson geometry and Azumaya loci of cluster algebrasAbstract: Roughly speaking, cluster algebra is a commutative algebra obtained from taking the intersection of Laurent polynomial rings associated a "seed". When a cluster […]
Title - Stability Theorems for the Width Abstract - In this talk, I'll discuss some recent and ongoing work about the stability of min-max widths of spheres under various lower […]
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 […]
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 […]