Seminars and Colloquia by Series

Friday, September 22, 2017 - 15:00 , Location: Skiles 154 , Jiaqi Yang , Georgia Tech , Organizer: Jiaqi Yang
We will continue from last week's talk. There are many advances toward proof of Arnold diffusion in Mather's setting. In particular, we will study an approach based on recent work of Marian-Gidea and Jean-Pierre Marco.
Friday, September 22, 2017 - 13:55 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Friday, September 22, 2017 - 12:05 , Location: Skiles 006 , Francesco Di Plinio , University of Virginia , Organizer: Amalia Culiuc
It is a conjecture of Zygmund that the averages of a square integrable function over line segments oriented along a Lipschitz vector field on the plane converge pointwise almost everywhere. This statement is equivalent to the weak L^2 boundedness of the directional maximal operator along the vector field. A related conjecture, attributed to Stein, is the weak L^2 boundedness of the directional Hilbert transform taken along a Lipschitz vector field. In this talk, we will discuss recent partial progress towards Stein’s conjecture obtained in collaboration with I. Parissis, and separately with S. Guo, C. Thiele and P. Zorin-Kranich. In particular, I will discuss the recently obtained sharp bound for the Hilbert transform along finite order lacunary sets in two dimensions and possible higher dimensional generalization
Thursday, September 21, 2017 - 15:05 , Location: Skiles 006 , Edgar Dobriban , University of Pennsylvania, Wharton School , dobriban@wharton.upenn.edu , Organizer: Mayya Zhilova
We consider the $\textit{linearly transformed spiked model}$, where observations $Y_i$ are noisy linear transforms of unobserved signals of interest $X_i$: $$Y_i = A_i X_i + \varepsilon_i,$$ for $i=1,\ldots,n$. The transform matrices $A_i$ are also observed. We model $X_i$ as random vectors lying on an unknown low-dimensional space. How should we predict the unobserved signals (regression coefficients) $X_i$? The naive approach of performing regression for each observation separately is inaccurate due to the large noise. Instead, we develop optimal linear empirical Bayes methods for predicting $X_i$ by "borrowing strength'' across the different samples. Our methods are applicable to large datasets and rely on weak moment assumptions. The analysis is based on random matrix theory. We discuss applications to signal processing, deconvolution, cryo-electron microscopy, and missing data in the high-noise regime. For missing data, we show in simulations that our methods are faster, more robust to noise and to unequal sampling than well-known matrix completion methods. This is joint work with William Leeb and Amit Singer from Princeton, available as a preprint at arxiv.org/abs/1709.03393.
Thursday, September 21, 2017 - 13:30 , Location: Skiles 005 , Laszlo Vegh , London School of Economics , L.Vegh@lse.ac.uk , Organizer: Prasad Tetali
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation.Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics. Specifically, we give a generic reduction to structured instances that resemble but are more general than those arising from node-weighted metrics. For those instances, we then solve Local-Connectivity ATSP, a problem known to be equivalent (in terms of constant-factor approximation) to the asymmetric traveling salesman problem.This is joint work with Ola Svensson and Jakub Tarnawski.
Wednesday, September 20, 2017 - 13:55 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
The theory of braids has been very useful in the study of (classical) knot theory. One can hope that higher dimensional braids will play a similar role in higher dimensional knot theory. In this talk we will introduce the concept of braided embeddings of manifolds, and discuss some natural questions about them.
Wednesday, September 20, 2017 - 13:55 , Location: Skiles 005 , Robert Kesler , Georgia Tech , Organizer: Shahaf Nitzan
 Magyar, Stein, and Wainger proved a discrete variant in Zd of the continuous spherical maximal theorem in Rd for all d ≥ 5. Their argument proceeded via the celebrated “circle method” of Hardy, Littlewood, and Ramanujan and relied on estimates for continuous spherical maximal averages via a general transference principle. In this talk, we introduce a range of sparse bounds for discrete spherical maximal averages and discuss some ideas needed to obtain satisfactory control on the major and minor arcs. No sparse bounds were previously known in this setting.
Series: Other Talks
Wednesday, September 20, 2017 - 13:00 , Location: Skiles 255 , David Krejcirik , Czech Technical University , krejcirik@ujf.cas.cz , Organizer:

NOTE:  This is the first in a forthcoming series of colloquia in quantum mathematical physics that will take place this semester.  The series is a spin-off of last year's QMath conference, and is intended to be of broad interest to people wanting to know the state of the art of current topics in mathematical physics.

We shall make an overview of the interplay between the geometry of tubular neighbourhoods of Riemannian manifold and the spectrum of the associated Dirichlet Laplacian.  An emphasis will be put on the existence of curvature-induced eigenvalues in bent tubes and Hardy-type inequalities in twisted tubes of non-circular cross-section.  Consequences of the results for physical systems modelled by the Schroedinger or heat equations will be discussed.
Wednesday, September 20, 2017 - 12:10 , Location: Skiles 006 , Tim Duff , GA Tech , Organizer: Timothy Duff
An academic webpage allows you to better communicate your work and help you become more recognizable in your research community. We'll talk about the very basics of how to set one up and what you should put on it----no prior experience necessary! Please bring a laptop if you can---as usual, refreshments will be provided.
Series: PDE Seminar
Tuesday, September 19, 2017 - 15:05 , Location: Skiles 006 , Chenchen Mou , UCLA , muchenchen@math.ucla.edu , Organizer: Yao Yao
The talk is about a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain. This is a joint work with R. Gong and A. Swiech.

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