Seminars and Colloquia by Series

Hopf fibrations for oceanic waves and turbulent pipe flows

Series
Math Physics Seminar
Time
Thursday, September 18, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Francesco Fedele – School of Civil and Environmental Engineering, Georgia Tech
I propose a generalization of Hopf fibrations to quotient the streamwise translation symmetry of water waves and turbulent pipe flows viewed as dynamical systems. In particular, I exploit the geometric structure of the associated high dimensional state space, which is that of a principal fiber bundle. Symmetry reduction analysis of experimental data reveals that the speeds of large oceanic crests and turbulent bursts are associated with the dynamical and geometric phases of the corresponding orbits in the fiber bundle. In particular, in the symmetry-reduced frame I unveil a pattern-changing dynamics of the fluid structures, which explains the observed speed u ≈ Ud+Ug of intense extreme events in terms of the geometric phase velocity Ug and the dynamical phase velocity Ud associated with the orbits in the bundle. In particular, for oceanic waves Ug/Ud~-0.2 and for turbulent bursts Ug/Ud~0.43 at Reynolds number Re=3200.

Those Kissing Cousins, Polynomials and Entire Functions of Exponential Type

Series
Research Horizons Seminar
Time
Wednesday, September 17, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
D. Lubinsky – Georgia Tech Math Department
There is a long standing asymptotic relationship in several areas of analysis, between polynomials and entire functions of exponential type. Many extremal problems for polynomials of degree n turn into analogous extremal problems for entire functions of exponential type, as the degree n approaches infinity. We discuss some of the old such as Bernstein's constant on approximation of |x|, and recent work on Plancherel-Polya and Nikolskii inequalities.

Physics Colloquium - Hydrodynamics and Quantum Anomalies

Series
Other Talks
Time
Monday, September 15, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Pettit Bldg., Conf Room 102 A&B
Speaker
Dam Thanh Son – University of Chicago

Please Note: Host: Shina Tan, School of Physics, Georgia Tech

Hydrodynamics is the theory describing collective behaviors of fluids and gases. It has a very long history and is usually considered to belong to the realm of classical physics. In recent years, it has been found that, in many cases, hydrodynamics can manifest a purely quantum effect --- anomalies. We will see how this new appreciation of the interplay between quantum and classical physics has emerged, unexpectedly, through the idea of gauge/gravity duality, which originates in modern string theory. I will briefly mention the possible relevance of the new findings to the physics of the quark gluon plasma.

4-manifolds can be surface bundles in many ways

Series
Geometry Topology Seminar
Time
Monday, September 15, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nick Salter – University of Chicago
An essential feature of the theory of 3-manifolds fibering over the circle is that they often admit infinitely many distinct structures as a surface bundle. In four dimensions, the story is much more rigid: a given 4-manifold admits only finitely many fiberings as a surface bundle over a surface. But how many is “finitely many”? Can a 4-manifold possess three or more distinct surface bundle structures? In this talk, we will survey some of the beautiful classical examples of surface bundles over surfaces with multiple fiberings, and discuss some of our own work. This includes a rigidity result showing that a class of surface bundles have no second fiberings whatsoever, as well as the first example of a 4-manifold admitting three distinct surface bundle structures, and our progress on a quantitative version of the “how many?” question.

Moment bounds and concentration for sample covariance operators in Banach spaces

Series
Stochastics Seminar
Time
Thursday, September 11, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Vladimir Koltchinskii – School of Mathematics, Georgia Tech
We will discuss sharp bounds on moments and concentration inequalities for the operator norm of deviations of sample covariance operators from the true covariance operator for i.i.d. Gaussian random variables in a separable Banach space. Based on a joint work with Karim Lounici.

Chern-Simons theory and knot invariants

Series
Geometry Topology Student Seminar
Time
Wednesday, September 10, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Paprocki – Georgia Tech
We will present an introduction to gauge theory and classical Chern-Simons theory, a 3-dimensional topological gauge field theory whose quantization yields new insights about knot invariants such as the Jones polynomial. Then we will give a sketch of quantum Chern-Simons theory and how Witten used it as a 3-dimensional method to obtain the Jones polynomial, as well as how it may be used to obtain other powerful knot and 3-manifold invariants. No physics background is necessary.

Existence of strong solutions to Compressible Navier-Stokes equations with degenerate viscosities and vacuum

Series
PDE Seminar
Time
Tuesday, September 9, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shengguo Zhu – Georgia Tech
We identify sufficient conditions on initial data to ensure the existence of a unique strong solution to the Cauchy problem for the Compressible Navier-Stokes equations with degenerate viscosities and vacuum (such as viscous Saint-Venants model in $\mathbb{R}^2$). This is a recent work joint with Yachun Li and Ronghua Pan.

Variable Selection Consistency of Linear Programming Discriminant Estimator

Series
High-Dimensional Phenomena in Statistics and Machine Learning Seminar
Time
Tuesday, September 9, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dong Xia – School of Mathematics, Georgia Tech
The linear programming discriminant(LPD) estimator is used in sparse linear discriminant analysis for high dimensional classification problems. In this talk we will give a sufficient condition for the variable selection property of the LPD estimator and our result provides optimal bound on the requirement of sample size $n$ and magnitude of components of Bayes direction.

Log-Sobolev Inequalities and Their Applications

Series
Analysis Working Seminar
Time
Monday, September 8, 2014 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
George Kerchev – School of Math –
This talk will concern Log-Sobolev inequalities and their applications. We will discuss connections to exponential convergence of Markov semigroups, the Poincare inequality and Gaussian concentration. It's the first part of a series.

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