Title: Non-uniqueness of mean curvature flow Abstract: The smooth mean curvature flow often develops singularities, making weak solutions essential for extending the flow beyond singular times, as well as having applications for geometry and topology. Among various weak formulations, the level set flow method is notable for ensuring long-time existence and uniqueness. However, this comes […]
Title: Wait! That Cannot Be RightAbstract: In this talk proofs will be presented that contain an incorrect step or include an incorrect assumption. This will lead us to prove concepts that are clearly false. This incorrect step or assumption will not be obvious, in fact the proofs will be presented in a way to try […]
Title: The Utility of L-FunctionsAbstract: Following Serre, we will explain how L-functions and potential automorphy results enter the proof of the Sato–Tate conjecture for elliptic curves. If we have time remaining, we will explain how the same approach can be used to prove the Chebotarev density theorem.
Title: Minimal Log Discrepancy and Orbifold Curves.Abstract: We show that the minimal log discrepancy of any isolated Fano cone singularity is at most the dimension of the variety. This is based on its relation with dimensions of moduli spaces of orbifold rational curves. We also propose a conjectural characterization of weighted projective spaces as Fano orbifolds in […]
This event will feature a panel of faculty from our math department to provide support for students seeking to learn more about the process of applying to graduate school in mathematics. It will help students choose schools based on interests and gain unique insights into what the whole process entails.
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: 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: TBA Abstract: TBA