SEPTEMBER SPEAKERS


September 11th, 12pm
Speaker: Ido Kanter , Bar-Ilan University
Title: "Ultrafast Physical random number generators"
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.
Location: Hill Center Building (Busch Campus), Room 705


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




September 11th, 2pm
Speaker: Jozsef Beck, Rutgers
Title: "How long does it take for a large dynamical system to reach complete randomness?"
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".
Location: Hill Center Building (Busch Campus), Room 705


September 18th, 12pm
Speaker: Ofer Zeitouni, University of Minnesota
Title: "Freezing and decorated Poisson point processes"
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.
Location: Hill Center Building (Busch Campus), Room 705


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


September 18th, 2pm
Speaker: Ivan Sudakov, University of Utah
Title: " Critical Phenomena in Planetary Climate: Statistical Physics Approach"
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.
Location: Hill Center Building (Busch Campus), Room 705





OCTOBER SPEAKERS


October 2nd, 12pm
Speaker: Yanyan Li, Rutgers
Title: "The Nirenberg problem and its generalizations: A unified approach"
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 $P_\sigma(v)= K v^{ \frac{n+2\sigma}{n-2\sigma} }$ on the standard sphere $S^n$ for $\sigma\in (0, n/2)$, where $P_\sigma$ is the conformal fractional Laplacian of order $2\sigma$. 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.
Location: Hill Center Building (Busch Campus), Room 705


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



October 2nd, 2pm
Speaker: Alex Kontorovich, Rutgers
Title: "Dynamics and Number Theory"
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.
Location: Hill Center Building (Busch Campus), Room 705



October 9th, 12pm
Speaker: Giovanni Gallavotti, Rutgers
Title: "Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model"
Abstract: We construct different equivalent non-equilibrium statistical ensembles in a $N$-degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. The purpose is to test conjectures on a theory of ensembles in non equilibrium statistical mechanics and turbulence as well as the chaotic hypothesis and the fluctuation relation. This leads to the proposal that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.
Location: Hill Center Building (Busch Campus), Room 705


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



October 9th, 2pm
Speaker: Roderich Tumulka, Rutgers
Title: "Novel type of Hamiltonians without ultraviolet divergence for quantum field theories"
Abstract: In quantum field theories, the terms in the Hamiltonian governing particle creation and annihilation are usually ultraviolet (UV) divergent. The problem can be circumvented by either discretizing space or attributing a nonzero radius to the electron (or other particles). I describe a novel way of defining a Hamiltonian, to our knowledge not previously considered in the literature; these Hamiltonians are well defined, involve particle creation and annihilation, treat space as a continuum, and give radius zero to electrons. They are defined in the particle-position representation of Fock space by means of a new kind of boundary condition on the wave function, which we call an interior-boundary condition (IBC) because it relates values of the wave function on a boundary of configuration space to values in the interior. Here, the relevant configuration space is that of a variable number of particles, the relevant boundary consists of the collision configurations (i.e., those at which two or more particles meet), and the relevant interior point lies in a sector with fewer particles. I will describe results about Schrodinger and Dirac operators with IBCs. This is joint work with Stefan Teufel, Julian Schmidt, and Jonas Lampart.
Location: Hill Center Building (Busch Campus), Room 705