Seminars and Colloquia by Series

Friday, April 12, 2013 - 15:05 , Location: Skiles 006 , Vieri Mastropietro , Università degli Studi di Milano , Organizer: Federico Bonetto
Several low dimensional interacting fermionic systems, including g raphene and spin chains, exhibit remarkable universality properties in the c onductivity, which can be rigorously established under certain conditions by combining Renormal ization Group methods with Ward Identities.
Wednesday, April 10, 2013 - 14:00 , Location: Skiles 005 , Jacopo de Simoi , Universita' di Roma Tor Vergata , Organizer: Federico Bonetto
Lots of attention and research activity has been devoted to partially hyperbolic dynamical systems and their perturbations in the past few decades; however, the main emphasis has been on features such as stable ergodicity and accessibility rather than stronger statistical properties such as existence of SRB measures and exponential decay of correlations. In fact, these properties have been previously proved under some specific conditions (e.g. Anosov flows, skew products) which, in particular, do not persist under perturbations. In this talk, we will construct an open (and thus stable for perturbations) class of partially hyperbolic smooth local diffeomorphisms of the two-torus which admit a unique SRB measure satisfying exponential decay of correlations for Hölder observables. This is joint work with C. Liverani
Friday, April 5, 2013 - 15:05 , Location: Skiles 006 , Pierluigi Falco , California State University, Northridge , Organizer: Federico Bonetto
The lattice, two dimensional, Coulomb gas is the prototypical model of Statistical Mechanics displaying the 'Kosterlitz-Thouless' phase transition. In this seminar I will discuss conjectures, results and works in progress about this model.
Friday, March 29, 2013 - 15:00 , Location: Skiles 006 , Nikolai Chernov , UAB , Organizer: Federico Bonetto
We study a gas of N hard disks in a box with semi-periodic boundary conditions. The unperturbed gas is hyperbolic and ergodic (these facts are proved for N=2 and expected to be true for all N>2). We study various perturbations by "twisting" the outgoing velocity at collisions with the walls. We show that the dynamics tends to collapse to various stable regimes, however we define the perturbations and however small they are.
Friday, March 8, 2013 - 15:00 , Location: Skiles 006 , Rafael Benguria , P. Universidad Católica de Chile , rbenguri@fis.puc.cl , Organizer:
In this talk I will discuss a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms
Friday, February 22, 2013 - 15:00 , Location: Skiles 006 , David Borthwick , Emory University , davidb@mathcs.emory.edu , Organizer:
Abstract:  In this talk we will survey some recent developments in the scattering theory of complete, infinite-volume manifolds with ends modeled on quotients of hyperbolic space.  The theory of scattering resonances for such spaces is in many ways parallel to the classical case of eigenvalues on a compact Riemann surface.  However, it is only relatively recently that progress has been made in understanding the distribution of these resonances.  We will give some introduction to the theory of resonances in this context and try to sketch this recent progress.  We will also discuss some interesting outstanding conjectures and present numerical evidence related to these.
Friday, February 1, 2013 - 16:00 , Location: Skiles 006 , Evans Harrell , Georgia Tech , harrell@math.gatech.edu , Organizer:
I'll discuss two methods for finding bounds on sums of graph eigenvalues (variously for the Laplacian, the renormalized Laplacian, or the adjacency matrix). One of these relies on a Chebyshev-type estimate of the statistics of a subsample of an ordered sequence, and the other is an adaptation of a variational argument used by P. Kröger for Neumann Laplacians.  Some of the inequalities are sharp in suitable senses.  This is ongoing work with J. Stubbe of EPFL
Thursday, December 6, 2012 - 16:05 , Location: Skiles 005 , Amit Einav , University of Cambridge , Organizer: Michael Loss
 In this talk we will discuss the definition of chaoticity and entropic chaoticity, as well as the background that led us to define these quantities, mainly Kac's model and the Boltzmann equation. We will then proceed to investigate the fine balance required for entropic chaoticity by exploring situations where chaoticity is valid, but not entropic chaoticity. We will give a general method to construct such states as well as two explicit example, one of which is quite surprising.
Wednesday, September 19, 2012 - 15:00 , Location: Howey N110 , Dwight Barkley , Mathematics Institute, University of Warwick , Organizer:

Host: Predrag Cvitanovic

More than 125 years ago Osborne Reynolds launched the quantitative study of turbulent transition as he sought to understand the conditions under which fluid flowing through a pipe would be laminar or turbulent. Since laminar and turbulent flow have vastly different drag laws, this question is as important now as it was in Reynolds' day. Reynolds understood how one should define "the real critical value'' for the fluid velocity beyond which turbulence can persist indefinitely. He also appreciated the difficulty in obtaining this value. For years this critical Reynolds number, as we now call it, has been the subject of study, controversy, and uncertainty. Now, more than a century after Reynolds pioneering work, we know that the onset of turbulence in shear flows is properly understood as a statistical phase transition. How turbulence first develops in these flows is more closely related to the onset of an infectious disease than to, for example, the onset of oscillation in the flow past a body or the onset of motion in a fluid layer heated from below. Through the statistical analysis of large samples of individual decay and proliferation events, we at last have an accurate estimate of the real critical Reynolds number for the onset of turbulence in pipe flow, and with it, an understanding of the nature of transitional turbulence. This work is joint with: K. Avila, D. Moxey, M. Avila, A. de Lozar, and B. Hof.
Monday, April 30, 2012 - 12:05 , Location: Skiles 006 , Emanuel Indrei , University of Texas , Organizer: Michael Loss
The relative isoperimetric inequality inside an open, convex cone C states that under a volume constraint, the ball intersected the cone minimizes the perimeter inside C. In this talk, we will show how one can use optimal transport theory to obtain this inequality, and we will prove a corresponding sharp stability result. This is joint work with Alessio Figalli.

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