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 […]
Weyl law improvement on product of Zoll manifold
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 and Title TBD
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.