Title: The geometry of singular Kahler-Einstein metricsAbstract: The existence of a Kahler-Einstein metric can be a powerful tool to study complex manifolds. To use similar methods in the study of singular varieties, we need to understand the geometry of singular Kahler-Einstein metrics. I will discuss what some of the basic questions are, as well as […]
Title: Two-row Delta Springer varietiesAbstract: I will discuss the geometry and topology of a certain family of so-called Delta Springer varieties from an explicit, diagrammatic point of view. These singular varieties were introduced by Griffin—Levinson—Woo in 2021 in order to give a geometric realization of an expression that appears in the t = 0 case of […]
Title: Weak homotopy types of finite spaces Abstract: Can you construct an example of a topological space with only 4 points whose fundamental group is isomorphic to the group of integers Z? Upon first glance, our intuitions about finite subspaces of R^n would suggest that a space with finitely many points cannot admit homotopically interesting […]
Title: Restriction and local smoothing estimates using decoupling and two-ends inequalities.Abstract: I will discuss restriction estimates and local smoothing estimates derived from decoupling theorems and two-ends inequalities, with a focus on the differences between these two problems. Specifically, I will introduce the wave packet density, which is the key to the induction on scales argument […]
Title: On the Global Well-posedness and Scattering of the Schrödinger and Wave equations on the Hyperbolic Spaces
Title: Wall crossing for moduli of stable pairs.Abstract: Hassett showed that there are natural reduction morphisms between moduli spaces of weighted pointed stable curves when we reduce weights. I will discuss some joint work with Ziquan Zhuang which constructs similar morphisms between moduli of stable pairs in higher dimension.
Title: Real groups, symmetric varieties, quantum groups, and Langlands duality Abstract: I will explain a connection between relative Langlands duality and geometric Langlands on real forms of the projective line (i.e. the real projective line or the twistor P1), then explain recent results using this to answer some questions in Langlands duality for real groups and symmetric […]
Title: Monoidal complete Segal spaces. Abstract: Viewing a monoid as a category with a single object allows us to encode the binary operation using the properties of composition and associativity inherent in any category. In this talk, we use this idea to explore the relationship between (∞,1)-categories with a monoidal structure and (∞,2)-categories with one […]
Title: Finite-Time Singularities of the Ricci Flow on Kähler SurfacesAbstract: By work of Song-Weinkove, it is understood that the Ricci flow on any Kähler surface can canonically be continued through singularities in a continuous way until its volume collapses. This talk will discuss recent progress in understanding a more detailed picture of the singularity formation […]
Title: Automorphic Representations and Quantum Logic Gates Abstract: Any construction of a quantum computer requires finding a good set of universal quantum logic gates: abstractly, a finite set of matrices in U(2^n) such that short products of them can efficiently approximate arbitrary unitary transformations. The 2-qubit case n=2 is of particular practical interest. I will […]