Seminars and Colloquia by Series

Bounds on the eigenvalues of Laplace-Beltrami operators and Witten Laplacians on Riemannian manifolds

Series
Math Physics Seminar
Time
Friday, April 19, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ahmad El Soufi – Université François Rabelais, Tours, France –

Please Note: El Soufi will be visiting Harrell for the week leading up to this seminar

We shall survey some of the classical and recent results giving upper bounds of the eigenvalues of the Laplace-Beltrami operator on a compact Riemannian manifold (Yang-Yau, Korevaar, Grigor'yan-Netrusov-Yau, etc.). Then we discuss extensions of these results to the eigenvalues of Witten Laplacians associated to weighted volume measures and investigate bounds of these eigenvalues in terms of suitable norms of the weights.

Universal Conductivity Properties In Many Body Physics

Series
Math Physics Seminar
Time
Friday, April 12, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Vieri Mastropietro – Università degli Studi di Milano
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.

Fast-slow partially hyperbolic systems beyond averaging.

Series
Math Physics Seminar
Time
Wednesday, April 10, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jacopo de Simoi – Universita' di Roma Tor Vergata
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

Statistical Mechanics of the Two-Dimensional Coulomb Gas

Series
Math Physics Seminar
Time
Friday, April 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pierluigi Falco – California State University, Northridge
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.

Stable regimes for hard disks in a channel with twisting walls

Series
Math Physics Seminar
Time
Friday, March 29, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nikolai Chernov – UAB
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.

Indirect Coulomb Energy for Two-Dimensional Atoms

Series
Math Physics Seminar
Time
Friday, March 8, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rafael Benguria – P. Universidad Católica de Chile –
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

Resonances for manifolds with hyperbolic ends

Series
Math Physics Seminar
Time
Friday, February 22, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Borthwick – Emory University –
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.

Bounds on sums of graph eigenvalues

Series
Math Physics Seminar
Time
Friday, February 1, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Evans Harrell – Georgia Tech –
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

A few Ways to Destroy Entropic Chaoticity

Series
Math Physics Seminar
Time
Thursday, December 6, 2012 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amit Einav – University of Cambridge
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.

The onset of turbulence in pipe flow

Series
Math Physics Seminar
Time
Wednesday, September 19, 2012 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey N110
Speaker
Dwight Barkley – Mathematics Institute, University of Warwick

Please Note: 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.

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