Title: Generalized Bondage Number: The k-synchronous bondage number of a GraphAbstract: In this talk I will introduce the notions of domination, domination number, and bondage number on a graph. We will generalize the notion to k-synchronous bondage number, mainly the case when k = 2. We will present k-synchronous bondage number for several graph classes.
Title: A characterization of uniruled Kähler manifolds.Abstract: We adapt Bost's algebraicity characterization to the situation of a germ in a compact Kähler manifold. As a consequence, we extend the algebraic integrability criteria of Campana-Paun and of Druel to foliations on compact Kähler manifolds. As an application, we prove that a compact Kähler manifold is uniruled if and […]
Title: Tame Betti local Langlands Abstract: Representations of finite Weyl groups can be realized inside the top cohomology of Springer fibers. By replacing cohomology by equivariant K-theory, Kazhdan and Lusztig classified tamely ramified representations of p-adic groups. Arkhipov and Bezrukavnikov categorified the Kazhdan-Lusztig isomorphism by proving a coherent realization of the affine Hecke category. I […]
Title: A Comparison of Two Supercharacter TheoriesAbstract: In 2008, P. Diaconis and I.M. Isaacs introduced a generalization of classical character theory, which they called supercharacter theory. Let X be a partitioning of the irreducible characters of a finite group G such that the trivial character is in its own block of this partition. Let Y […]
Title: Gradescope Grading and Rubric Creation. Abstract: “Gradescope Grading and Rubric Creation” is designed for Mathematics teaching assistants. This workshop aims to support TA's in building consistent Gradescope rubrics, determining key grading criteria, and identifying opportunities for partial credit. By the end of the workshop, teaching assistants will have practiced using a Gradescope rubric with […]
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 […]