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.
Seminars and Colloquia by Series
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: Other Talks
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.
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: 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: 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: 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
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: 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.
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.