Seminars and Colloquia by Series

The Alexander module and categorification

Series
Geometry Topology Working Seminar
Time
Friday, March 2, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jen Hom – Georgia Tech
In this series of talks, we will study the relationship between the Alexander module and the bordered Floer homology of the Seifert surface complement. In particular, we will show that bordered Floer categorifies Donaldson's TQFT description of the Alexander module. No prior knowledge of the Alexander module or Heegaard Floer homology will be assumed.

Non-smooth boundary value problems

Series
School of Mathematics Colloquium
Time
Friday, March 2, 2018 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jill Pipher – Brown University
The regularity properties of solutions to linear partial differential equations in domains depend on the structure of the equation, the degree of smoothness of the coefficients of the equation, and of the boundary of the domain. Quantifying this dependence is a classical problem, and modern techniques can answer some of these questions with remarkable precision. For both physical and theoretical reasons, it is important to consider partial differential equations with non-smooth coefficients. We’ll discuss how some classical tools in harmonic and complex analysis have played a central role in answering questions in this subject at the interface of harmonic analysis and PDE.

Matroids and log-concavity

Series
Student Algebraic Geometry Seminar
Time
Friday, March 2, 2018 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 254
Speaker
Marcel Celaya – Georgia Tech –
In this talk we will discuss the paper of Adiprasito, Huh, and Katz titled "Hodge Theory for Combinatorial Geometries," which establishes the log-concavity of the characteristic polynomial of a matroid.

Cryptography: From ancient times to a post-quantum age

Series
Stelson Lecture Series
Time
Thursday, March 1, 2018 - 18:00 for 1 hour (actually 50 minutes)
Location
Klaus Lecture Auditorium 1443
Speaker
Jill Pipher – Brown University
How is it possible to send encrypted information across an insecure channel (like the internet) so that only the intended recipient can decode it, without sharing the secret key in advance? In 1976, well before this question arose, a new mathematical theory of encryption (public-key cryptography) was invented by Diffie and Hellman, which made digital commerce and finance possible. The technology advances of the last twenty years bring new and urgent problems, including the need to compute on encrypted data in the cloud and to have cryptography that can withstand the speed-ups of quantum computers. In this lecture, we will discuss some of the history of cryptography, as well as some of the latest ideas in "lattice" cryptography which appear to be quantum resistant and efficient.

Classification of knots in 3-sphere

Series
Geometry Topology Student Seminar
Time
Wednesday, February 28, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki Min – GaTech
I will introduce the notion of satellite knots and show that a knot in a 3-sphere is either a torus knot, a satellite knot or a hyperbolic knot.

A sharp Schroedinger maximal estimate in two dimensions

Series
Analysis Seminar
Time
Wednesday, February 28, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xiumin Du – Institute for Advanced Study –
Joint with Guth and Li, recently we showed that the solution to the free Schroedinger equation converges to its initial data almost everywhere, provided that the initial data is in the Sobolev space H^s(R^2) with s>1/3. This is sharp up to the endpoint, due to a counterexample by Bourgain. This pointwise convergence problem can be approached by estimates of Schroedinger maximal functions, which have some similar flavor as the Fourier restriction estimates. In this talk, I'll first show how to reduce the original problem in three dimensions to an essentially two dimensional one, via polynomial partitioning method. Then we'll see that the reduced problem asks how to control the size of the solution on a sparse and spread-out set, and it can be solved by refined Strichartz estimates derived from l^2 decoupling theorem and induction on scales.

How to Make a Black Hole

Series
PDE Seminar
Time
Tuesday, February 27, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xinliang An – University of Toronto –
Black holes are predicted by Einstein's theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being. In this talk, with tools from hyperbolic PDE, quasilinear elliptic equations, geometric analysis and dynamical systems, we will prove that, through a nonlinear focusing effect, initially low-amplitude and diffused gravitational waves can give birth to a black hole region in our universe. This result extends the 1965 Penrose’s singularity theorem and it also proves a conjecture of Ashtekar on black-hole thermodynamics. Open problems and new directions will also be discussed.

Complex zeros and algorithms in hard problems of combinatorial counting

Series
ACO Colloquium
Time
Tuesday, February 27, 2018 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Barvinok – University of Michigan –
Many hard problems of combinatorial counting can be encoded as problems of computing an appropriate partition function. Formally speaking, such a partition function is just a multivariate polynomial with great many monomials enumerating combinatorial structures of interest. For example, the permanent of an nxn matrix is a polynomial of degree n in n^2 variables with n! monomials enumerating perfect matchings in the complete bipartite graph on n+n vertices. Typically, we are interested to compute the value of such a polynomial at a real point; it turns out that to do it efficiently, it is very helpful to understand the behavior of complex zeros of the polynomial. This approach goes back to the Lee-Yang theory of the critical temperature and phase transition in statistical physics, but it is not identical to it: thinking of the phase transition from the algorithmic point of view allows us greater flexibility: roughly speaking, for computational purposes we can freely operate with “complex temperatures”. I plan to illustrate this approach on the problems of computing the permanent and its versions for non-bipartite graphs (hafnian) and hypergraphs, as well as for computing the graph homomorphism partition function and its versions (partition functions with multiplicities and tensor networks) that are responsible for a variety of problems on graphs involving colorings, independent sets, Hamiltonian cycles, etc. (This is the first (overview) lecture; two more will follow up on Thursday 1:30pm, Friday 3pm of the week. These two lectures are each 80 minutes' long.)

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