Seminars and Colloquia by Series

Wednesday, September 5, 2018 - 12:55 , Location: Skiles 006 , Santosh Vempala , Georgia Institute of Technology , vempala@cc.gatech.edu , Organizer: Galyna Livshyts
The concentration of Lipschitz functions around their expectation is a classical topic and continues to be very active. In these talks, we will discuss some recent progress in detail, including:  A tight log-Sobolev inequality for isotropic logconcave densities A unified and improved large deviation inequality for convex bodies An extension of the above to Lipschitz functions (generalizing the Euclidean squared distance)The main technique of proof is a simple iteration (equivalently, a Martingale process) that gradually transforms any density into one with a Gaussian factor, for which isoperimetric inequalities are considerably easier to establish.  (Warning: the talk will involve elementary calculus on the board, sometimes at an excruciatingly slow pace).   Joint work with Yin Tat Lee. 
Tuesday, September 4, 2018 - 11:00 , Location: Skiles 006 , Sara van de Geer , ETH Zurich , Organizer: Mayya Zhilova
The colloquium will be the second lecture of the TRIAD Distinguished Lecture Series by Prof. Sara van de Geer. For further information please see http://math.gatech.edu/events/triad-distinguished-lecture-series-sara-van-de-geer-0.
Monday, September 3, 2018 - 14:00 , Location: Skile 006 , None , None , Organizer: John Etnyre
Friday, August 31, 2018 - 15:00 , Location: None , None , None , Organizer: Lutz Warnke
Thursday, August 30, 2018 - 15:05 , Location: Skiles 006 , Andrew Nobel , University of North Carolina, Chapel Hill , Organizer: Mayya Zhilova
This talk concerns the description and analysis of a variational framework for empirical risk minimization. In its most general form the framework concerns a two-stage estimation procedure in which (i) the trajectory of an observed (but unknown) dynamical system is fit to a trajectory from a known reference dynamical system by minimizing average per-state loss, and (ii) a parameter estimate is obtained from the initial state of the best fit reference trajectory. I will show that the empirical risk of the best fit trajectory converges almost surely to a constant that can be expressed in variational form as the minimal expected loss over dynamically invariant couplings (joinings) of the observed and reference systems. Moreover, the family of joinings minimizing the expected loss fully characterizes the asymptotic behavior of the estimated parameters. I will illustrate the breadth of the variational framework through applications to the well-studied problems of maximum likelihood estimation and non-linear regression, as well as the analysis of system identification from quantized trajectories subject to noise, a problem in which the models themselves exhibit dynamical behavior across time. 
Thursday, August 30, 2018 - 12:00 , Location: Skiles 005 , Rose McCarty , University of Waterloo , Organizer: Robin Thomas
Vertex minors are a weakening of the notion of induced subgraphs that benefit from many additional nice properties. In particular, there is a vertex minor version of Menger's Theorem proven by Oum. This theorem gives rise to a natural analog of branch-width called rank-width. Similarly to the Grid Theorem of Robertson and Seymour, we prove that a class of graphs has unbounded rank-width if and only if it contains all "comparability grids'' as vertex minors. This is joint work with Jim Geelen, O-joung Kwon, and Paul Wollan.
Wednesday, August 29, 2018 - 12:55 , Location: Skiles 006 , Konstantin Tikhomirov , GeorgiaTech , Organizer: Konstantin Tikhomirov
We show that there is a symmetric n-dimensional convex set whose Banach--Mazur distance to the cube is bounded below by n^{5/9}/polylog(n). This improves previously know estimate due to S.Szarek, and confirms a conjecture of A.Naor. The proof is based on probabilistic arguments.
Wednesday, August 29, 2018 - 01:55 , Location: Skiles 154 , Michael Lacey , Georgia Tech , Organizer: Michael Lacey
Spherical averages, in the continuous and discrete setting, are a canonical example of averages over lower dimensional varieties. We demonstrate here a new approach to proving the sparse bounds for these opertators.  This approach is a modification of an old technique of Bourgain. 
Monday, August 27, 2018 - 14:30 , Location: Boyd , Akram Alishahi and Artem Kotelskiy , Columbia and Indiana University , Organizer: Caitlin Leverson
Wednesday, August 22, 2018 - 14:00 , Location: Skiles 005 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay

This theorem is one of earliest instance of the h-principle, and there will be a series of talks on it this semester.

The Whitney-Graustein theorem classifies immersions of the circle in the plane by their turning number. In this talk, I will describe a proof of this theorem, as well as a related result due to Hopf.

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