Mathematical Physics
Seminar

November Schedule

Organizer: Joel L. Lebowitz
lebowitz@math.rutgers.edu

Speaker: Abhay Ashtekar, Penn State University
Time/Place:Thursday 11/4, 11:30am, Serin 385 **(PLEASE NOTE ROOM CHANGE)**
Title: "Highlights of Loop Quantum Gravity"
Abstract: I will discuss a background independent approach to quantum gravity, based on a specific theory of quantum geometry. I will first describe its salient features and then, to illustrate the ramifications of quantum geometry, use it to address some fundamental issues concerning the big-bang and black holes. The talk will be addressed to non-specialists.

THERE WILL BE A BROWN BAG LUNCH BETWEEN THE TWO SEMINARS. COOKIES & COFFEE WILL BE PROVIDED. PLEASE BRING YOUR LUNCH.

Speaker: Tom Banks, Rutgers
Time/Place: Thursday 11/4, 1:30pm, SERIN 385 **(PLEASE NOTE ROOM CHANGE)**
Title: "Triumphs and Travails of String Theory"
Abstract: I will discuss the successes of string theory in constructing calculable models of quantum gravity in imaginary universes with exact super Poincare invariance and/or asymptotically Anti- de Sitter boundary conditions (appropriate for no-positive cosmological constant). I will show how non-abelian gauge invariance, and chiral fermions, similar to those which describe the standard model of particle physics, emerge from geometrical constructions in this framework. I will then discuss the problem of dealing with the real world, in which supersymmetry is broken and the cosmological constant is positive. I believe that the key ideas here will be the holographic principle and complementarity, concepts derived from our understanding of string theory.


Barry Simon's seminar has been canceled for Thursday, 11/11/04 at 11:30am. Please check back for rescheduling. THERE WILL BE NO BROWN BAG LUNCH TODAY.




Speaker: Holly Carley, Rutgers University
Time/Place:Thursday, 11/11, 1:30pm, Room 705
Title: "The strong-coupling limit for the ground state energy of aparticle harmonic oscillator interaction"
Abstract:Consider a quantum Hamiltonian for a particle interacting with a harmonic oscillator. Minimizing the energy over product states gives an upper bound on the ground state energy. Lieb observed the remarkable fact that for some couplings this is within 1 of the ground state energy. We will investigate improvements of this estimate in the large coupling limit.


**INFORMAL SEMINAR**
Please note day & time!!

Speaker: A. Giuliani, INFN Roma II/Rutgers University
Time/Place: MONDAY, 11/15 2:30, Room 705
Title: "Anomalous critical exponents in 2d Ising models with four spin interactions"
Abstract: A wide class of perturbations of the 2D Ising model can be exactly mapped into a system of 1D interacting fermions. This allows to study thermodynamic quantities of such spin models at the critical point in terms of correlation functions of a massless fermionic system at 0 temperature via fermionic Renormalization Group. Following this strategy, we study the location of the critical points and the critical behaviour of the specific heat in the Ashkin-Teller model, which is a system in which two Ising layers interact via a four spin interaction.
**SPECIAL SEMINAR**
Please note day!!

Speaker: A. Sokal, NYU
Time/Place:WEDNESDAY, 11/17 1:30pm, Room 705
Title:"Open Problems on the Interface between Statistical Mechanics and Combinatorics"
Abstract:This talk is an informal attempt to describe some exciting open problems (and a few exciting results obtained in recent years) lying at the interface between Statistical Mechanics and Combinatorics. They mostly have to do with the Potts model in one guise or another.


Speaker: David Ruelle, IHES, France
Time/Place:, Thursday 11/18 11:30am, Room 705
Title:"Linear response away from equilibrium"
Abstract:The linear response in nonequilibrium statistical mechanics can be described mathematically as the differentiation of an SRB measure with respect to a parameter. For certain types of dynamics (uniformly hyperbolic) one gets a very satisfactory description, with a modified fluctuation-dissipation theorem, and analyticity properties corresponding to "causality". For other systems (Henon-like), "causality" seems to break down, and things are less simple. What does this mean?

THERE WILL BE A BROWN BAG LUNCH BETWEEN THE TWO SEMINARS. COOKIES & COFFEE WILL BE PROVIDED. PLEASE BRING YOUR LUNCH.





Speaker: Barry Simon, California Tech (visiting NYU)
Time/Place: Thursday 11/18, 1:30pm, Room 705
Title: "The Sharp Form of the Strong Szego Theorem"
Abstract: This talk will discuss a proof of the Strong Szego theorem on the second term in the asymptotics of Toeplitz determinants. After a brief discussion of the history, I'll discuss the elementary argument that reduces the sharp (optimal) result to the case of analytic symbols. I'll then present a new proof of the theorem in the analytic case. I'll present the necessary background from the theory of orthogonal polynomials on the unit circle along the way.