november 07 schedule</title?></head> <body background="calmwinterbkg.jpg"> <center><img src="acorns-n-leaves.gif"> <br> <h1>Mathematical Physics Seminar <br> November Schedule</h1><p> <img src="acorns-n-leaves.gif"> </center> <hr width=500> <br> <b>Speaker</b>: Eric Carlen, Rutgers University<br> <b>Date/Time/Place</b>: Thursday, November 1, 2007 12:00pm Hill 705<br> <b>Title</b>: Convexity and concavity of certain trace functionals, and quantum entropy inequalities.<br> <b>Abstract</b>: This talk will present the proof of the convexity and concavity of certain trace functionals. These results had been conjectured in an earlier paper by Lieb and myself, and attracted the attention of other researchers, some of whom doubted the conjectures. We have recently devised a proof, using a new variational principle, and this will be presented here, along with a discussion of the ultimate origins of the problem in the Wigner-Yanase-Dyson conjecture and the strong subadditivity of quantum entropy. <hr width=500> <br> <br> <b>Speaker</b>: D. Ruelle, IHES <br><b>Date/Time</b>: Thursday, November 8, 2007 12:00pm Hill 705<br> <b>Title</b>: Towards a General Response Theory<br> <b>Abstract</b>: For a system of statistical mechanics close to equilibrium one can define a response function. The Fourier transform of the response function is known as susceptibility. Due to causality, the susceptibility is analytic in the upper half-plane, and this gives the Kramers-Kronig dispersion relations. If one uses a nonequilibrium steady state for a system far from equilibrium, the Chaotic Hypothesis of Gallavotti-Cohen (i.e., hyperbolicity of the dynamics) implies that we still have analyticity of the susceptibility in the upper half-plane. For nonhyperbolic dynamics, however, singularities appear in the upper half-plane: an apparent "violation of causality" which remains to be interpreted physically. <hr width=500> <br> <br> <b>Speaker</b>: G. Gallavotti, Professor at Universit di Roma "La Sapienza"<br> <b>Date/Place/Time</b>: Thursday, November 8, 2007 Hill 705 2:00pm<br> <b>Title</b>: Fluctuations in nonequilibrium: classical and quantum.<br> <b>Abstract</b>: In classical systems it seems established that phase space contraction and entropy creation rate can be identified in stationary nonequilibria. This will be discussed in the light of possible extensions to quantum systems in stationary states and the corresponding theory of fluctuations. <hr width=500> <br> <br> <b>Speaker</b>: Jozsef Beck, Rutgers University<br> <b>Date/Time/Place</b>: Thursday, November 15, 2007 12:00pm Hill 705<br> <b>Title</b>: Shadows of dice playing: a general vague probabilistic conjecture in discrete mathematics<br> <b>Abstract</b>: I just finished the first draft of a new book with the title "Shadows of dice playing" and the subtitle is "a general vague ...". In the book I formulate a vague conjecture that I prefer to call the Solid-Liquid-Gas Conjecture. It says, roughly speaking, that discrete systems (in number theory, in combinatorics, etc.) are either "simple" (periodic, or have nested structure) or they exhibit full-blown "dice-randomness" with or without constraints. "Simple" corresponds to the "solid state of matter", "dice randomness without constraints" represents the gas state, and finally, "dice randomness with constraints" corresponds to the "liquid state". I will show several illustrations and a lot of evidence for the vague conjecture. The book is 230 pages long; of course I cannot explain everything; this talk is just an "appetizer". <hr width=500> <br> <br> <b>Speaker:</b> Jozsef Beck, Rutgers University <br> <b>Date/Time/Place:</b> Tuesday, November 20, 2007 12:00pm Hill 705 <br> <b>Title:</b> Shadows of dice playing: a general vague probabilistic conjecture in discrete mathematics (PART II). <br> <b>Abstract: </b> I just finished the first draft of a new book with the title ``Shadows of dice playing" and the subtitle is ``a general vague ...". In the book I formulate a vague conjecture that I prefer to call the Solid-Liquid-Gas Conjecture. It says, roughly speaking, that discrete systems (in number theory, in combinatorics, etc.) are either ``simple" (periodic, or have nested structure) or they exhibit full-blown ``dice-randomness" with or without constraints. ``Simple" corresponds to the ``solid state of matter", ``dice randomness without constraints" represents the gas state, and finally, "dice randomness with constraints" corresponds to the ``liquid state". I will show several illustrations and a lot of evidence for the vague conjecture. The book is 230 pages long; of course I cannot explain everything; this talk is just an ``appetizer". <center>THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00pm</center> <br><br> <b>Speaker:</b> Joel L. Lebowitz, Rutgers University <br> <b>Date/Place/Time:</b> Tuesday, November 20, 2007 Hill 705 2:00pm <br> <b>Title:</b> Time's Arrow and Boltzmann Entropy (PART II). <br> <b>Abstract:</b> In the world about us the past is distinctly different from the future. Milk spills but doesn't unspill; eggs splatter but do not unsplatter; waves break but do not unbreak; we always grow older, never younger. These processes all move in one direction in time - they are called "time-irreversible" and define the arrow of time. It is therefore very surprising that the relevant fundamental laws of nature make no such distinction between the past and the future. This in turn leads to a great puzzle - if the laws of nature permit all processes to be run backwards in time, why don't we observe them doing so? Why does a video of an egg splattering run backwards look ridiculous? Put another way: how can time-reversible motions of atoms and molecules, the microscopic components of material systems, give rise to the observed time-irreversible behavior of our everyday world? The resolution of this apparent paradox is due to Maxwell, Thomson and (particularly) Boltzmann. They did it, of course, in the context of classical mechanics. I will discuss their ideas also in the quantum mechanical context. <hr width=500> <br><br> <center><b>There will be no seminar Thursday, November 22, 2007</b></center> <br><br> <hr width=500> <b>Speaker</b> A. Sengupta, Rutgers University<br> <b>Date/Place/TIme</b>:November 29, 2007 12:00pm Hill 705<br> <b> Title </b>:TBA<br> <b>Abstract</b>:TBA <hr width=500> <br> <br> </html>