## Seminars and Colloquia by Series

Wednesday, February 14, 2018 - 13:55 , Location: Skiles 005 , , Georgia Institute of technology , Organizer: Galyna Livshyts
We study Balian-Low type theorems for finite signals in $\mathbb{R}^d$, $d\geq 2$.Our results are generalizations of S. Nitzan and J.-F. Olsen's recent work and show that a quantity closelyrelated to the Balian-Low Theorem has the same asymptotic growth rate, $O(\log{N})$ for each dimension $d$.  Joint work with Michael Northington.
Wednesday, February 14, 2018 - 12:10 , Location: Skiles 006 , , Georgia Tech , Organizer:
Some basic problems, notions and results of the Ergodic theory will be introduced. Several examples will be discussed.   It is also  a preparatory talk for the next day colloquium where finite time properties of dynamical and stochastic systems will be discussed rather than traditional questions all dealing with asymptotic in time properties.
Wednesday, February 14, 2018 - 11:00 , Location: Skiles 006 , , University of British Columbia , , Organizer: Michael Damron
I will discuss two projects concerning Mallows permutations, with Ander Holroyd, Tom Hutchcroft and Avi Levy.  First, we relate the Mallows permutation to stable matchings, and percolation on bipartite graphs. Second, we study the scaling limit of the cycles in the Mallows permutation, and relate it to diffusions and continuous trees.
Series: PDE Seminar
Tuesday, February 13, 2018 - 15:00 , Location: Skiles 006 , , Princeton University , , Organizer: Yao Yao
The SQG equation models the formation of fronts of hot and cold air. In a different direction this system was proposed as a 2D model for the 3D incompressible Euler equations. At the linear level, the equations are dispersive. As of today, it is not known if this equation can produce singularities. In this talk I will discuss some recent work on the global solutions of the SQG equation and related models for small data. Joint work with Diego Cordoba and Alex Ionescu.
Monday, February 12, 2018 - 14:00 , Location: Skiles 006 , Josh Sabloff , Haverford College , Organizer: John Etnyre
Lagrangian fillings of Legendrian knots are interesting objects that are related, on one hand, to the 4-genus of the underlying smooth knot and, on the other hand, to Floer-type invariants of Legendrian knots. Most work on Lagrangian fillings to date has concentrated on orientable fillings.  I will present some first steps in constructions of and obstructions to the existence of (decomposable exact) non-orientable Lagrangian fillings.  In addition, I will discuss links between the 4-dimensional crosscap number of a knot and the non-orientable Lagrangian fillings of its Legendrian representatives. This is joint work in progress with Linyi Chen, Grant Crider-Philips, Braeden Reinoso, and Natalie Yao.
Friday, February 9, 2018 - 15:00 , Location: Skiles 271 , Joan Gimeno , BGSMath-UB , Organizer: Jiaqi Yang
We are going to explain how invariant dynamical objects, such as (quasi)periodic orbits, can numerically be computed for Delay Differential Equations as well as their stability. To this end, we will use Automatic Differentiation techniques and iterative linear solvers with appropiate preconditioners. Additionally some numerical experiments will be presented to illustrate the approaches for each of those objects.This is joint work with A. Jorba.
Friday, February 9, 2018 - 15:00 , Location: Skiles 202 , Federico Bonetto , Georgia Tech , Organizer: Michael Loss
I'll report on a project, developed in collaboration with Michael Loss, to extend a very simple model of rarefied gas due to Mark Kac and use it to understand some basic issues of Equilibrium and Non-Equilibrium Statistical Mechanics.
Friday, February 9, 2018 - 13:05 , Location: Skiles 005 , , CS, MIT , , Organizer: He Guo
A lot of well-studied problems in CS Theory are about making “sketches” of graphs that occupy much less space than the graph itself, but where the shortest path distances of the graph can still be approximately recovered from the sketch. For example, in the literature on Spanners, we seek a sparse subgraph whose distance metric approximates that of the original graph. In Emulator literature, we relax the requirement that the approximating graph is a subgraph. Most generally, in Distance Oracles, the sketch can be an arbitrary data structure, so long as it can approximately answer queries about the pairwise distance between nodes in the original graph. Research on these objects typically focuses on optimizing the worst-case tradeoff between the quality of the approximation and the amount of space that the sketch occupies. In this talk, we will survey a recent leap in understanding about this tradeoff, overturning the conventional wisdom on the problem. Specifically, the tradeoff is not smooth, but rather it follows a new discrete hierarchy in which the quality of the approximation that can be obtained jumps considerably at certain predictable size thresholds. The proof is graph-theoretic and relies on building large families of graphs with large discrepancies in their metrics.
Friday, February 9, 2018 - 10:10 , Location: Skiles 254 , , Georgia Tech , , Organizer: Kisun Lee
As a continuation to last week's talk, we introduce the ring D of differential operators with complex coefficients, or the Weyl algebra. As we saw last week, the theory of the ring R, the ring of differential operators with rational function coefficients, is in many ways almost the same as the regular polynomial ring. The ring D however will look slightly different as its structure is much finer. We will look at filtrations, graded rings and Gröbner bases induced by weight vectors. Finally we will present an overview on the integration algorithm of holonomic D-modules and mention some applications.
Thursday, February 8, 2018 - 15:00 , Location: Skiles 006 , , Columbia University , Organizer: Mayya Zhilova
It has been conjectured that phenomena as diverse as the behavior of large "self-organizing" neural networks, and causality in standard model particle physics, can be explained by suitably rich algebras acting on themselves. In this talk I discuss the asymptotics of large causal tree diagrams that combine freely independent elements of such algebras. The Marchenko-Pastur law and Wigner's semicircle law are shown to emerge as limits of a normalized sum-over-paths of non-negative elements assigned to the edges of causal trees. The results are established in the setting of non-commutative probability. Trees with classically independent positive edge weights (random multiplicative cascades) were originally proposed by Mandelbrot as a model displaying the fractal features of turbulence. The novelty of the present work is the use of non-commutative (free) probability to allow the edge weights to take values in an algebra.