Mathematics Department - Mathematical Physics Seminar - Fall 2014

Mathematical Physics Seminar - Fall 2014



Organizer(s)

Joel Lebowitz, Michael Kiessling

Archive

Website

http://www.math.rutgers.edu/~lebowitz/Fall2013seminars.html



Upcoming Talks


Thursday, October 2nd

Yanyan Li, Rutgers University

"The Nirenberg problem and its generalizations: A unified approach"

Time: 12:00 PM
Location: Hill 705
Abstract: Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations $P_sigma(v)= K v^{ frac{n+2sigma}{n-2sigma} }$ on the standard sphere $S^n$ for $sigmain (0, n/2)$, where $P_sigma$ is the conformal fractional Laplacian of order $2sigma$. Finding positive solutions of these equations is equivalent to seeking metrics in the conformal class of the standard metric with prescribed certain curvatures. When $sigma=1$, it is the prescribing scalar curvature problem of the Nirenberg problem, and when $sigma=2$, it is the prescribing $Q-$curvature problem.

This is a joint work with Tianling Jin and Jingang Xiong.

BROWN BAG LUNCH AT 1PM


Thursday, October 2nd

Alex Kontorovich , Rutgers University

"Dynamics and Number Theory"

Time: 2:00 PM
Location: Hill 705
Abstract: We will give an informal discussion of some interactions between dynamics on homogeneous spaces and number theory, focussing specifically on conjectures of McMullen and Einsiedler-Lindenstrauss-Michel-Venkatesh.





Past Talks


Thursday, September 18th

Ivan Sudakov , University of Utah

"Critical Phenomena in Planetary Climate: Statistical Physics Approach"

Time: 2:00 PM
Location: Hill 705
Abstract: Planetary climate is the result of interactions between multiple physical systems. Current climate simulation techniques require much computational power based on scientifically sound but highly sophisticated computer models. Hence in many situations it is desirable to find simpler approaches to reduce the computational cost, in particular those based on classical statistical physics. I will explain the new approach that focuses on defining of free energy for the various patterns of tipping elements in the climate system (e.g., melt ponds, permafrost lakes, tropical convection patterns etc.). It is used to explain many of the recently observed geometric properties of these patterns, in particular the onset of pattern complexity and the distribution of pattern sizes. Moreover, applications of this approach help to identify phase transitions and other critical phenomena in the climate system, which may be of considerable theoretical interest.


Thursday, September 18th

Ofer Zeitouni, University of Minnesota

"Freezing and decorated Poisson point processes"

Time: 12:00 PM
Location: Hill 705
Abstract: The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point processes (SDPPP). In the proofs of those results, the Laplace functional of the limiting extremal process is shown to satisfy $L(theta_{y}f]=g(y-tau_{f})$ for any nonzero, nonnegative, compactly supported, continuous function $f$, where $theta_{y}$ is the shift operator, $tau_{f}$ is a real number that depends on $f$, and $g$ is a real function that is independent of $f$. We show that, under some assumptions, this property characterizes the structure of SDPPP. Moreover, when it holds, we show that $g$ has to be a convolution of the Gumbel distribution with some measure. The above property of the Laplace functional is closely related to a `freezing phenomenon' that is expected by physicists to occur in a wide class of log-correlated fields, and which has played an important role in the analysis of various models. Our results shed light on this intriguing phenomenon and provide a natural tool for proving an SDPPP structure in these and other models.

Joint work with Eliran Subag.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM.


Thursday, September 11th

Jozsef Beck , Rutgers University

"How long does it take for a large dynamical system to reach complete randomness?"

Time: 2:00 PM
Location: Hill 705
Abstract: Consider a large system of point billiards in a box, or many particles moving on a sphere, starting from some far-from equilibrium state (e.g., Big Bang). Assuming a reasonable initial velocity distribution (e.g., Maxwellian, meaning the 3-dim normal), how long does it take for the typical time evolution to reach "complete randomness"? We study "time-lapse randomness" and "snapshot randomness". I will talk about some surprising, counter-intuitive results, for which I cannot give a "plausible explanation".


Thursday, September 11th

Ido Kanter , Bar-Ilan University, Israel

"Ultrafast Physical random number generators"

Time: 12:00 PM
Location: Hill 705
Abstract: The generation of random bit sequences based on non-deterministic physical mechanisms is of paramount importance for cryptography and secure communications. High data rates also require extremely fast generation rates and robustness to external perturbations. Physical generators based on stochastic noise sources have been limited in bandwidth to 100 Mbit/s generation rates. We present a physical random bit generator, based on a chaotic semiconductor laser, having time-delayed self-feedback, which operates reliably at rates up to 300 Gbit/s. The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM.


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