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: 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 […]
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 […]
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 […]
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 […]