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Series: CDSNS Colloquium

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.

Series: Geometry Topology Seminar

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.

Monday, September 18, 2017 - 13:55 ,
Location: Skiles 005 ,
Prof. Nathan Kutz ,
University of Washington, Applied Mathematics ,
Organizer: Martin Short

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.

Series: Frontiers of Science

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

Series: School of Mathematics Colloquium

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.

Series: PDE Seminar

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.

Series: Research Horizons Seminar

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: Other Talks

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 - 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.

Series: Analysis Seminar

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: ACO Colloquium

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.

Series: Stochastics Seminar

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.

Series: Analysis Seminar

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

Series: Combinatorics Seminar

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.

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.