Abstract: This talk is aimed at a general mathematical audience. We begin by reviewing some mathematical history around some important ideas of von Neumann, and how they fit into the stream of mathematics. We then review some general techniques for dealing with spaces and algebras of Hilbert space operators, that is, with the ‘quantum analogue’ of functions and function spaces and algebras. There will be an emphasis on the theories of…

Mon, 12/02/2019 - 11:01am

Title: Mirror symmetry, geometry, and topological recursion
Abstract: Mirror symmetry was originally discovered by physicists. It reflects the symmetry in string theory, where two different versions of string theory called type IIA and type IIB string theory give rise to the same physics. Mathematicians became interested in this relationship around 1990 when Philip Candelas,Xenia de la Ossa, Paul Green, and Linda Parks showed that it could be…

Mon, 12/02/2019 - 10:59am

Title: Logarithmic Riemann-Hilbert Correspondences
Abstract: The classical Riemann-Hilbert Correspondence provides a deep connection between geometry and topology. In its simplest form it stipulates an equivalence between the categories of vector bundles with a flat connection on a complex manifold and local systems on the topological space underlying the manifold. If one allows the connection to have poles, the situation becomes considerably…

Mon, 12/02/2019 - 10:54am

Title: Exceptional splitting of abelian surfaces.
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if…

Mon, 11/18/2019 - 10:05am

Abstract:
In this talk, several topics from High-dimensional probability shall be discussed. This fascinating area is rich in beautiful problems, and several easy-to-state questions will be outlined. Further, some connections between them will be explained throughout the talk.
I shall discuss several directions of my research. One direction is invertibility properties of inhomogeneous random matrices: I will present sharp estimates on the small…

Wed, 10/09/2019 - 10:02am

Thu, 04/25/2019 - 2:58pm

Title: Combinatorics, Categorification, and Crystals
Abstract: Categorification attempts to replace algebraic and geometric structures with more general categories. It has enjoyed amazing successes, such as Khovanov homology categorifying the Jones polynomial, KLR algebras categorifying quantum groups, or Soergel bimodules categorifying Hecke algebras. The payoffs to finding these richer, higher categorical structures include applications like…

Fri, 04/05/2019 - 3:01pm

Fri, 03/22/2019 - 10:30am

Uniform Convergence is a one-woman play, written and performed by mathematics graduate student Corrine Yap. It juxtaposes the stories of two women trying to find their place in a white male-dominated academic world. The first is of historical Russian mathematician Sofia Kovalevskaya, who was lauded as a pioneer for women in science but only after years of struggle for recognition. Her life's journey is told through music and movement, in both…

Wed, 03/20/2019 - 9:45am

Colloquium/Conversation/Performance at the Dancz Center for New Music, Hugh Hogson School of Music
In live musical performance and open discussion, Marcus Miller and Rob Schneiderman demonstrate/explain analogies between the dynamics of the discovery/creation/learning of both Music and Mathematics. As a consequence of the abstract natures of Music and Mathematics these analogies can provide insight into other human disciplines. Marcus Miller…

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