All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
|January 28 (Th 4pm VV901)||Steven Sivek (Princeton)||The augmentation category of a Legendrian knot||Ellenberg|
|January 29||Ana Caraiani (Princeton)||Ellenberg|
|February 5||Takis Souganidis (University of Chicago)||Lin|
|February 12||Gautam Iyer (CMU)||Jean-Luc|
|February 19||Jean-François Lafont (Ohio State)||Dymarz|
|February 26||Hiroyoshi Mitake (Hiroshima university)||Tran|
|March 4||Guillaume Bal (Columbia University)||Li, Jin|
|March 11||Mitchell Luskin (University of Minnesota)||Mathematical Modeling of Incommensurate 2D Materials||Li|
|March 18||Ralf Spatzier (University of Michigan)||TBA||Dymarz|
|March 25||Spring Break|
|April 1||Chuu-Lian Terng (UC Irvine) -->||TBA -->||Mari-Beffa|
|April 8||Alexandru Ionescu (Princeton)||TBA||Wainger/Seeger|
|April 15||Igor Wigman (King's College - London)||Nodal Domains of Eigenfunctions||Gurevich/Marshall|
|April 22||Paul Bourgade (NYU)||TBA||Seppalainen/Valko|
|April 29||Randall Kamien (U Penn)||TBA||Spagnolie|
|May 6||Julius Shaneson (University of Pennsylvania)||TBA||Maxim/Kjuchukova|
January 28: Steven Sivek (Princeton)
Title: The augmentation category of a Legendrian knot
Abstract: A well-known principle in symplectic geometry says that information about the smooth structure on a manifold should be captured by the symplectic geometry of its cotangent bundle. One prominent example of this is Nadler and Zaslow's microlocalization correspondence, an equivalence between a category of constructible sheaves on a manifold and a symplectic invariant of its cotangent bundle called the Fukaya category.
The goal of this talk is to describe a model for a relative version of this story in the simplest case, corresponding to Legendrian knots in the standard contact 3-space. This construction, called the augmentation category, is a powerful invariant which is defined in terms of holomorphic curves but can also be described combinatorially. I will describe some interesting properties of this category and relate it to a category of sheaves on the plane. This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende, and Eric Maslow.
March 11: Mitchell Luskin (UMN)
Title: Mathematical Modeling of Incommensurate 2D Materials
Abstract: Incommensurate materials are found in crystals, liquid crystals, and quasi-crystals. Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the elastic, electronic, and optical properties of these materials. One of the main issues encountered in the mathematical modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. This leads to complex commensurate-incommensurate transitions and pattern formation.
Even basic concepts like the Cauchy-Born strain energy density, the electronic density of states, and the Kubo-Greenwood formulas for transport properties have not been given a rigorous analysis in the incommensurate setting. New approximate approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.