## Seminars and Colloquia by Series

Series
Math Physics Seminar
Time
Thursday, October 3, 2013 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Roger NicholsUniversity of Tennessee, Chattanooga
Following Kato, we define the sum, $H=H_0+V$, of two linear operators, $H_0$ and $V$, in a fixed Hilbert space in terms of its resolvent. In an abstract theorem, we present conditions on $V$ that guarantee $\text{dom}(H_0^{1/2})=\text{dom}(H^{1/2})$ (under certain sectorality assumptions on $H_0$ and $H$). Concrete applications to non-self-adjoint Schr\"{o}dinger-type operators--including additive perturbations of uniformly elliptic divergence form partial differential operators by singular complex potentials on domains--where application of the abstract theorem yields $\text{dom}(H^{1/2})=\text{dom}((H^{\ast})^{1/2})$, will be presented. This is based on joint work with Fritz Gesztesy and Steve Hofmann.

### Localization for the quasi 1D operators

Series
Math Physics Seminar
Time
Friday, September 27, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stanislav MolchanovUNC Charlotte
The talk will present several recent results on the singular and pure point spectra for the (random or non-random) Schrӧdinger operators on the graphs or the Riemannian manifolds of the “small dimensions”. The common feature of all these results is the existence in the potential of the infinite system of the “bad conducting blocks”, for instance, the increasing potential barriers (non-percolating potentials). The central idea of such results goes to the classical paper by Simon and Spencer. The particular examples will include the random Schrӧdinger operators in the tube (or the surface of the cylinder), Sierpinski lattice etc.

### The Kac Model Coupled to a Thermostat

Series
Math Physics Seminar
Time
Thursday, September 19, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ranjini VaidyanathanGeorgia Tech
We consider a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an inﬁnite gas at thermal equilibrium at inverse temperature \beta. The system admits the canonical distribution at inverse temperature \beta as the unique equilibrium state. We prove that the any initial distribution approaches the equilibrium distribution exponentially fast both by computing the gap of the generator of the evolution, in a proper function space, as well as by proving exponential decay in relative entropy. We also show that the evolution propagates chaos and that the one-particle marginal, in the large system limit, satisﬁes an effective Boltzmann-type equation. This is joint work with Federico Bonetto and Michael Loss.

### 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 SoufiUniversité 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 MastropietroUniversità 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 SimoiUniversita&amp;#039; 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 FalcoCalifornia 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 BenguriaP. 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 BorthwickEmory 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.