Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Spring 2016

date	speaker	title	host(s)
January 22
January 28 (Th 4pm VV901)	Steven Sivek (Princeton)	The augmentation category of a Legendrian knot	Ellenberg
January 29	Ana Caraiani (Princeton)
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

Abstracts

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.