Seminars and Colloquia Schedule

Periodic Driving at High Frequencies of an Impurity in the Isotropic XY Chain

Series
CDSNS Colloquium
Time
Monday, September 18, 2017 - 12:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Livia Corsi – Georgia Institute of Technology –
I will consider the isotropic XY quantum chain with a transverse magnetic field acting on a single site and analyze the long time behaviour of the time-dependent state of the system when a periodic perturbation drives the impurity. It has been shown in the early 70’s that, in the thermodynamic limit, the state of such system obeys a linear time-dependent Schrodinger equation with a memory term. I will consider two different regimes, namely when the perturbation has non-zero or zero average, and I will show that if the magnitute of the potential is small enough then for large enough frequencies the state approaches a periodic orbit synchronized with the potential. Moreover I will provide the explicit rate of convergence to the asymptotics. This is a joint work with G. Genovese.

Data-driven discovery of governing equations and physical laws

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Nathan Kutz – University of Washington, Applied Mathematics
The emergence of data methods for the sciences in the last decade has been enabled by the plummeting costs of sensors, computational power, and data storage. Such vast quantities of data afford us new opportunities for data-driven discovery, which has been referred to as the 4th paradigm of scientific discovery. We demonstrate that we can use emerging, large-scale time-series data from modern sensors to directly construct, in an adaptive manner, governing equations, even nonlinear dynamics, that best model the system measured using modern regression techniques. Recent innovations also allow for handling multi-scale physics phenomenon and control protocols in an adaptive and robust way. The overall architecture is equation-free in that the dynamics and control protocols are discovered directly from data acquired from sensors. The theory developed is demonstrated on a number of canonical example problems from physics, biology and engineering.

Taut branched surfaces from veering triangulations

Series
Geometry Topology Seminar
Time
Monday, September 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Landry – Yale –
Let M be a closed hyperbolic 3-manifold with a fibered face \sigma of the unit ball of the Thurston norm on H_2(M). If M satisfies a certain condition related to Agol’s veering triangulations, we construct a taut branched surface in M spanning \sigma. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher. I will not assume knowledge of the Thurston norm, branched surfaces, or veering triangulations.

Scientific Computing in the Movies and Beyond

Series
Frontiers of Science
Time
Monday, September 18, 2017 - 18:00 for 1 hour (actually 50 minutes)
Location
Room 1005, Roger A. and Helen B. Krone Engineered Biosystems Building (EBB)
Speaker
Joseph M. Teran – UCLA Math
New applications of scientific computing for solid and fluid mechanics problems include simulation of virtual materials in movie special effects and virtual surgery. Both disciplines demand physically realistic dynamics for materials like water, smoke, fire, and soft tissues. New algorithms are required for each area. Teran will speak about the simulation techniques required in these fields and will share some recent results including: simulated surgical repair of biomechanical soft tissues; extreme deformation of elastic objects with contact; high resolution incompressible flow; and clothing and hair dynamics. He will also discuss a new algorithm used for simulating the dynamics of snow in Disney’s animated feature film, “Frozen”.More information at https://www.math.gatech.edu/hg/item/594422

Elastoplasticity Applications in Movie Special Effects

Series
School of Mathematics Colloquium
Time
Tuesday, September 19, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joseph Teran – UCLA Math
Simulation of hyperelastic materials is widely adopted in the computer graphics community for applications that include virtual clothing, skin, muscle, fat, etc. Elastoplastic materials with a hyperelastic constitutive model combined with a notion of stress constraint (or feasible stress region) are also gaining increasing applicability in the field. In these models, the elastic potential energy only increases with the elastic partof the deformation decomposition. The evolution of the plastic part is designed to satisfy the stress constraint. Perhaps the most common example of this phenomenon is denting of an elastic shell. However, other very powerful examples include frictional contact material interactions. I will discuss some of the mathematical aspects of these models and present some recent results and examples in computer graphics applications.

Stochastic Representations for Solutions to Nonlocal Bellman Equations

Series
PDE Seminar
Time
Tuesday, September 19, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chenchen Mou – UCLA –
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.

Academic Webpage Workshop

Series
Research Horizons Seminar
Time
Wednesday, September 20, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tim Duff – GA Tech
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.

Quolloquium: Spectral geometry of quantum waveguides

Series
Other Talks
Time
Wednesday, September 20, 2017 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
David Krejcirik – Czech Technical University –

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.

Braided embeddings of manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, September 20, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech
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.

Sparse Bounds for Discrete Spherical Maximal Averages

Series
Analysis Seminar
Time
Wednesday, September 20, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Kesler – Georgia Tech
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.

A constant-factor approximation algorithm for the asymmetric traveling salesman problem

Series
ACO Colloquium
Time
Thursday, September 21, 2017 - 13:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Laszlo Vegh – London School of Economics –
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.

Optimal prediction in the linearly transformed spiked model

Series
Stochastics Seminar
Time
Thursday, September 21, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Edgar Dobriban – University of Pennsylvania, Wharton School –
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.

Maximal averages and singular integrals along vector fields in higher dimension

Series
Analysis Seminar
Time
Friday, September 22, 2017 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Francesco Di Plinio – University of Virginia
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

No Seminar: Ravi Kannan speaking in The IDEaS Seminar Series

Series
Combinatorics Seminar
Time
Friday, September 22, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
-
Speaker
- – -
Clash with "The IDEaS Seminar Series": the talk of Ravi Kannan at 3pm on "Topic Modeling: Proof to Practice" might of interest (Location: TSRB Auditorium) -- Topic Modeling is used in a variety of contexts. This talk will outline from first principles the problem, and the well-known Latent Dirichlet Al-location (LDA) model before moving to the main focus of the talk: Recent algorithms to solve the model-learning problem with provable worst-case error and time guarantees. We present a new algorithm which enjoys both provable guarantees as well performance to scale on corpora with billions of words on a single box. Besides corpus size, a second challenge is the growth in the number of topics. We address this with a new model in which topics lie on low-dimensional faces of the topic simplex rather than just vertices.