Seminars and Colloquia by Series

The Talbot effect in a non-linear dynamics.

Series
School of Mathematics Colloquium
Time
Tuesday, November 18, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Luis Vega – BCAM-Basque Center for Applied Mathematics (Scientific Director) and University of the Basque Country UPV/EHU –
In the first part of the talk I shall present a linear model based on the Schrodinger equation with constant coefficient and periodic boundary conditions that explains the so-called Talbot effect in optics. In the second part I will make a connection of this Talbot effect with turbulence through the Schrodinger map which is a geometric non-linear partial differential equation.

Dynamics of inertial particles with memory: an application of fractional calculus

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Mohammad Farazmand – GA Tech Physics
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. I discuss the governing equations of motion for the inertial particles, i.e. the Maxey-Riley equation, including a fractional order derivative in time. Then I show that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is O(\epsilon)-close to the fluid velocity, where 0<\epsilon<<1 is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity.

Localization sequences in the algebraic K-theory of ring spectra

Series
Geometry Topology Seminar
Time
Monday, November 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Gepner – Purdue University
The algebraic K-theory of the sphere spectrum, K(S), encodes significant information in both homotopy theory and differential topology. In order to understand K(S), one can apply the techniques of chromatic homotopy theory in an attempt to approximate K(S) by certain localizations K(L_n S). The L_n S are in turn approximated by the Johnson-Wilson spectra E(n) = BP[v_n^{-1}], and it is not unreasonable to expect to be able to compute K(BP). This would lead inductively to information about K(E(n)) via the conjectural fiber sequence K(BP) --> K(BP) --> K(E(n)). In this talk, I will explain the basics of the K-theory of ring spectra, define the ring spectra of interest, and construct some actual localization sequences in their K-theory. I will then use trace methods to show that it the actual fiber of K(BP) --> K(E(n)) differs from K(BP), meaning that the situation is more complicated than was originally hoped. All this is joint work with Ben Antieau and Tobias Barthel.

Embeddings of manifolds and contact manifolds V

Series
Geometry Topology Working Seminar
Time
Friday, November 14, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
This is the fifth of several talks discussing embeddings of manifolds. I will discuss some general results for smooth manifolds, but focus on embeddings of contact manifolds into other contact manifolds. Particular attention will be paid to embeddings of contact 3-manifolds in contact 5-manifolds. I will discuss two approaches to this last problem that are being developed jointly with Yanki Lekili.

Connes distance and aperiodic order

Series
Math Physics Seminar
Time
Friday, November 14, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jean Savinien – University of Lorraine, Metz, France
We build a family of spectral triples for a discrete aperiodic tiling space, and derive the associated Connes distances. (These are non commutative geometry generalisations of Riemannian structures, and associated geodesic distances.) We show how their metric properties lead to a characterisation of high aperiodic order of the tiling. This is based on joint works with J. Kellendonk and D. Lenz.

Moduli of Tropical Plane Curves

Series
Algebra Seminar
Time
Friday, November 14, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Ralph Morrison – Berkeley
Smooth curves in the tropical plane correspond to unimodulartriangulations of lattice polygons. The skeleton of such a curve is ametric graph whose genus is the number of lattice points in the interior ofthe polygon. In this talk we report on work concerning the followingrealizability problem: Characterize all metric graphs that admit a planarrepresentation as a smooth tropical curve. For instance, about 29.5 percentof metric graphs of genus 3 have this property. (Joint work with SarahBrodsky, Michael Joswig, and Bernd Sturmfels.)

Math is in the eye of the beholder

Series
Applied and Computational Mathematics Seminar
Time
Friday, November 14, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Andre Martinez-Finkelshtein – Universidad de Almería
The medical imaging benefits from the advances in constructiveapproximation, orthogonal polynomials, Fourier and numerical analysis,statistics and other branches of mathematics. At the same time, the needs of the medical diagnostic technology pose new mathematical challenges. This talk surveys a few problems, some of them related to approximation theory, that have appeared in my collaboration with specialists studying some pathologies of the human eye, in particular, of the cornea, such as:- reconstruction of the shape of the cornea from the data collected bykeratoscopes- implementation of simple indices of corneal irregularity- fast and reliable computation of the through-focus characteristics of a human eye.

Singularity formation in Compressible Euler equations (Part III)

Series
PDE Working Seminar
Time
Thursday, November 13, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ronghua Pan – GeorgiaTech –
Compressible Euler equations describe the motion of compressible inviscid fluid. Physically, it states the basic conservation laws of mass, momentum, and energy. As one of the most important examples of nonlinear hyperbolic conservation laws, it is well-known that singularity will form in the solutions of Compressible Euler equations even with small smooth initial data. This talk will discuss some classical results in this direction, including some most recent results for the problem with large initial data.

Combining Riesz bases

Series
Job Candidate Talk
Time
Thursday, November 13, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shahaf Nitzan – Kent State University
Orthonormal bases (ONB) are used throughout mathematics and its applications. However, in many settings such bases are not easy to come by. For example, it is known that even the union of as few as two intervals may not admit an ONB of exponentials. In cases where there is no ONB, the next best option is a Riesz basis (i.e. the image of an ONB under a bounded invertible operator). In this talk I will discuss the following question: Does every finite union of rectangles in R^d, with edges parallel to the axes, admit a Riesz basis of exponentials? In particular, does every finite union of intervals in R admit such a basis? (This is joint work with Gady Kozma).

Random Matrix Models, Non-intersecting random paths, and the Riemann-Hilbert Analysis

Series
School of Mathematics Colloquium
Time
Thursday, November 13, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Andre Martinez-Finkelshtein – Universidad de Almería
Random matrix theory (RMT) is a very active area of research and a greatsource of exciting and challenging problems for specialists in manybranches of analysis, spectral theory, probability and mathematicalphysics. The analysis of the eigenvalue distribution of many random matrix ensembles leads naturally to the concepts of determinantal point processes and to their particular case, biorthogonal ensembles, when the main object to study, the correlation kernel, can be written explicitly in terms of two sequences of mutually orthogonal functions.Another source of determinantal point processes is a class of stochasticmodels of particles following non-intersecting paths. In fact, theconnection of these models with the RMT is very tight: the eigenvalues of the so-called Gaussian Unitary Ensemble (GUE) and the distribution ofrandom particles performing a Brownian motion, departing and ending at the origin under condition that their paths never collide are, roughlyspeaking, statistically identical.A great challenge is the description of the detailed asymptotics of these processes when the size of the matrices (or the number of particles) grows infinitely large. This is needed, for instance, for verification of different forms of "universality" in the behavior of these models. One of the rapidly developing tools, based on the matrix Riemann-Hilbert characterization of the correlation kernel, is the associated non-commutative steepest descent analysis of Deift and Zhou.Without going into technical details, some ideas behind this technique will be illustrated in the case of a model of squared Bessel nonintersectingpaths.

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