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: 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: 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: 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: 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: 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 […]
Title: Double Categories Abstract: This talk will give an introduction to double categories, double pseudofunctors, companions, conjoints, and some of their properties together with interesting examples and applications.
Abstract - Lecture 3 (lecture 2 will take place on March 24th at the Analysis & PDE seminar, see https://sites.google.com/view/hopkins-pde-seminar for details)In this series of lectures, we will explore viscosity solutions to fully nonlinear elliptic equations, following the foundational book of L. Caffarelli and X. Cabr´e in Fully Nonlinear Elliptic Equations (AMS Colloquium Publications, 1995). Our primary goal […]
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 the construction of the univeral left fibration, the Yoneda embedding and Yoneda lemma, a study of cofinal functors, Quillen's Theorem A, and first steps in […]