University of Virginia Mathematical Physics Seminar 2013-14

September 4 No meeting
September 11 Organizational meeting
September 18 Speaker: Ira Herbst (UVa)
Title: Exponential decay of eigenfunctions of elliptic partial differential operators (I)
Abstract: For eigenfunctions in the generalized N-body problem of quantum mechanics there is in general a countable closed set of decay rates possible for each eigenvalue. For a fixed N-body Hamiltonian the actual decay rate will vary with the addition of an N-particle interaction potential which decays at infinity. In this joint work with Erik Skibsted, we consider eigenfunctions of higher order self-adjoint partial differential operators on R^d. We look at the simplest case where the only x-dependence is in the zeroth order term which decays at infinity. We determine algebraically the possible decay rates and prove these are the only ones which can occur.
September 25 Speaker: Ira Herbst (UVa)
Title: Exponential decay of eigenfunctions of elliptic partial differential operators (II)
Abstract: See talk (I) in the series.
October 2 Speaker: Abdelmalek Abdesselam (UVa)
Title: Introduction to rigorous perturbative renormalization (I)
Abstract: In this series of lectures I will explain some of the mathematics behind perturbative renormalization which is used by physicists in their quantum field theory calculations. In particular I will show how Zimmermann's forest formula arises as the explicit solution of the implicit function theorem in the sense of formal power series. The presentation will be rather elementary and self-contained. No prior knowledge of quantum field theory will be needed.
October 9 Speaker: Abdelmalek Abdesselam (UVa)
Title: Introduction to rigorous perturbative renormalization (II)
Abstract: See talk (I) in the series.
October 16 Speaker: Abdelmalek Abdesselam (UVa)
Title: Introduction to rigorous perturbative renormalization (III)
Abstract: See talk (I) in the series.
October 23 Speaker: Ajay Chandra (UVa)
Title: Gradient Random Fields and the Helffer-Sjöstrand Random Walk Representation (I)
Abstract: This will be a basic notions talk. Gradient Random Fields are natural models for random surfaces, phase interfaces, and elasticity. I will give an overview of what is rigorously understood about these models. I will also describe the Helffer-Sjöstrand Random Walk Representation which allows one to analyze these random fields by studying a random walk in a dynamic random environment. The relevant references are Deuschel, Giacomin, and Ioffe - PTRF 2000 along with Naddaf and Spencer CMP 1997.
October 30 Speaker: Ira Herbst (UVa)
Title: Exponential decay of eigenfunctions of elliptic partial differential operators (III)
Abstract: See talk (I) in the series.
November 6 Speaker: Rajinder Mavi (UVa)
Title: Density estimates for nonmonotonic Anderson model (I)
Abstract: Multiscale analysis schemes for the classic Anderson model involve a Wegner estimate controlling the density of eigenvalues for the ill-behaved portions of the lattice. The classic Wegner estimate depends critically on the monotonicity properties of the model. Recently there have been extensions of results of this type into nonmonotonic Anderson models, such as a block Hamiltonian model and alloy models. In this talk we discuss one such method which is not based on multiscale arguments.
November 13 Speaker: Ajay Chandra (UVa)
Title: Gradient Random Fields and the Helffer-Sjöstrand Random Walk Representation (II)
Abstract: See talk (I) in the series.
November 20 Speaker: Rajinder Mavi (UVa)
Title: Density estimates for nonmonotonic Anderson model (II)
Abstract: See talk (I) in the series.
November 27 THANKSGIVING RECESS
December 4 Speaker: Hao Shen (Princeton University)
Title: Renormalization group by conditional expectations and dipole gas revisited
Abstract: We discuss a new renormalization group method based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one directly integrates Gaussian fields inside domains at all scales conditioning on the fields outside these domains, rather than making a multiscale decomposition of the Gaussian covariance as in the earlier methods. We apply this method to the model of classical dipole gas on the lattice.
December 11 Speaker: Rajinder Mavi (UVa)
Title: Density estimates for nonmonotonic Anderson model (III)
Abstract: See talk (I) in the series.
December 18 SEMESTER BREAK
January 15 No meeting
January 22 Organizational meeting
January 29 No meeting
February 5 No meeting
February 12 Speaker: Larry Thomas (UVa)
Title: Recent work on invariant measures for stochastic dissipative PDEs (I)
Abstract: I will review some recent work of Jaksic, Nersesyan, Pillet and Shirikyan on invariant measures for parabolic stochastic pde's as well as my own work for a stochastic wave equation. Included will be some discussion of entropy production and the Gallavotti-Cohen relation.
February 19 Speaker: Ira Herbst (UVa)
Title: The analyticty radius for solutions of the Navier-Stokes equations
Abstract: I will report on some (old) work on the growth rate of spatial analyticity properties of solutions of the Navier-Stokes equations.
February 26 Speaker: Larry Thomas (UVa)
Title: Recent work on invariant measures for stochastic dissipative PDEs (II)
Abstract: See talk (I) in the series.
March 5 Speaker: Gianluca Guadagni (UVa)
Title: Pre Scheduled Random Arrivals (PSRA) with exponentially distributed delays (I)
Abstract: I will consider an arrival process where scheduled arrivals are subject to random variations. The model is a bivariate Markov chain. I will discuss the case where the delays are exponentially distributed, for which we have a functional equation for the bivariate generating function. We do not have the solution yet, but I will show some of the different approaches we are trying to solve it. This is join work with C. Lancia, S. Ndreca, and B. Scoppola.
March 12 SPRING RECESS
March 19 TALK CANCELLED
March 26 Speaker: Martin Lohmann (ETH, Zürich)
Title: Cluster expansions for uncondensed many Boson systems (I)
Abstract: The grand canonical partition function, at chemical potential μ (critical or subcritical), of a system of bosons with weak repulsive interaction U is traditionally investigated - in the physics literature and, more recently, also rigorously - with the help of coherent state functional integrals. If μ < 0 is at unit distance from the critical point μ* ~ Û(0) > 0, these are small perturbations (not ultralocal) of single scale complex Gaussian measures. If μ < μ* approaches μ*, a finite number of new scales appear. We describe, in a general setting, cluster expansions that can be used to analyse such perturbations.
March 28* Speaker: Martin Lohmann (ETH, Zürich)
DIFFERENT TIME AND LOCATION: Friday Mar 28, 3:30pm-4:30pm in KER 317
Title: Cluster expansions for uncondensed many Boson systems (II)
Abstract: See talk (I) in the series.
April 2 Speaker: Gianluca Guadagni (UVa)
Title: Pre Scheduled Random Arrivals (PSRA) with exponentially distributed delays (II)
Abstract: See talk (I) in the series.
April 9 No meeting
April 16 Speaker: Rajinder Mavi (UVa)
Title: Dynamics in many body quantum systems (I)
Abstract: We discuss the Lieb-Robinson bound of controlling propagations in many body quantum systems. This bound was originally formulated for spin systems where each spin has finitely many degrees of freedom. Recent extensions include cases of coupled harmonic and certain anharmonic many body systems. We further discuss applications and dynamical localization in many body systems.
April 23 Speaker: Rajinder Mavi (UVa)
Title: Dynamics in many body quantum systems (II)
Abstract: See talk (I) in the series.

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