Title: Giving Students Useful Feedback. Abstract: "Giving Students Useful Feedback" is designed for Mathematics teaching assistants. This workshop aims to enhance TA's skills in providing effective and constructive feedback to students. By the end of the workshop, teaching assistants will be able to evaluate the effectiveness of examples of feedback and create feedback for students […]
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 […]
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 […]
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 […]
Title: Towards a birational geometric version of the monodromy conjecture.Abstract: The monodromy conjecture of Denef—Loeser is a conjecture in singularity theory that predicts that given a complex polynomial f, and any pole s of its motivic zeta function, exp(2πis) is a "monodromy eigenvalue" associated to f. I will formulate a "birational geometric" version of the conjecture, and […]
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 geometry is the study of smooth curves (informally bent lines) and surfaces (informally bent paper) inside of three-dimensional space.In this talk, we will define and […]
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 every Kakeya set has Minkowski and Hausdorff dimension n. We prove this conjecture in R^3 as a consequence of a more general statement about union […]
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 algebra satisfies some compatibility condition, M. Gekhtman, M. Shapiro, and A. Vainshtein showed that one can connect a Poisson bracket to the cluster algebra. In […]
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 curvature bounds. Some of this is joint with Davi Maximo and Paul Sweeney Jr.
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 integration bee, and other fun activities planned! Come by for a fun time!