Markus Kunze, Mathematisches Institut Universitat Koln
"Twist Maps and Very Fast Ping Pong"
Time: 2:00 PM
Location: Hill 705
Abstract: Twist maps are very important in dynamical systems, and in particular in the realm of K.A.M. (Kolmogorov-Arnold-Moser) theory. First it is explained how such maps arise and why they are a natural object to study. Afterwards we consider the Fermi-Ulam ping pong system (not to be confused with the Fermi-Pasta-Ulam chain) and try to determine how likely it is that the ball can reach infinite speed. Depending on the forcing function, this will lead to maps which cannot be treated by means of KAM theory or Aubry-Mather theory.
This is joint work with R. Ortega, Granada.)
Thursday, October 8th
Peter Alexandre Morozov , Rutgers University
"Statistical mechanics of random walks, with application to molecular evolution"
Time: 12:00 PM
Location: Hill 705
Abstract: Understanding properties of transport in networks and other complex media is crucial for quantitative analysis of numerous biological, physical, social and technological systems, from protein-protein interactions in biology to the World Wide Web. While transport on networks with unweighted edges can be described using scaling techniques, few analytical results are available for networks with weighted and directed edges, which appear naturally in evolutionary dynamics, chemical reactions, and protein folding. In this talk I will describe an efficient recursive approach for studying continuous-time random walks on weighted networks and fitness or energy landscapes of arbitrary complexity. Using simple examples, I will discuss the importance of non-exponential waiting time distributions, memory, and course-graining in first-passage processes. Finally, I will apply our approach to the problem of protein adaptation. Specifically, I will investigate how structural coupling between protein folding and binding (the fact that most proteins can only function when folded) gives rise to evolutionary coupling between the traits of folding stability and binding strength, facilitating the emergence of evolutionary "spandrels" (features that appear through adaptation even though the feature itself does not contribute
to the organism's fitness).
THERE WILL BE A BROWN BAG LUNCH FROM 1-2:00PM
Thursday, October 1st
Markus Kunze
"Yet another criterion for global existence in the 3D relativistic Vlasov-Maxwell system"
Time: 2:00 PM
Location: Hill 705
Abstract: The relativistic Vlasov-Maxwell system describes the time evolution of a
classical plasma in position-momentum phase space. Since the particles
can move at relativistic speeds, the motion of a single particle is governed
by the Lorentz force, whereas the self-generated electric and magnetic fields
are described by Maxwell's equations. The theory of existence of smooth
solution was initiated by Glassey and Strauss in the eighties, but an
unrestricted
result on global existence of solutions is still not available. We will
review the
state of the art and present a new criterion for global existence, which in
particular applies if a moment bound of order larger than three is available.
Thursday, October 1st
Clement Mouhot , University of Cambridge
"Holder continuity of solutions to Vlasov-Fokker-Planck type equations with rough coefficients"
Time: 12:00 PM
Location: Hill 705
Abstract: THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM
Thursday, September 24th
Jeffry Kahn , Rutgers University
"Asymptotics independent of structure"
Time: 2:00 PM
Location: Hill 705
Abstract: We'll be interested in situations in which enumerative information for a large discrete system is nearly determined by relatively simple parameters of the system; thus even very different systems will in some respects behave similarly if the parameters in question agree. (One may view such behavior as a reflection of weak long range interactions.)
We'll discuss a few examples of this type and try to mention a few more that are conjecturally so.
Thursday, September 17th
Soren Petrat, Institute of Science and Technology in Austria
"Derivation of Mean-Field Dynamics for Fermions"
Time: 2:00 PM
Location: Hill 705
Abstract: I present recent results about the derivation of the time-dependent Hartree(-Fock) equations from the Schroedinger equation for fermions in a mean-field limit. I introduce and discuss different scaling limits that were proposed for such a derivation. Several new methods were recently developed for tackling this kind of problems and I will focus on introducing the one I used myself in recent works. This method is based on controlling a well-chosen functional by estimating certain transition amplitudes in the Fermi gas. The functional is directly related to the trace norm difference of reduced density matrices and the estimates lead to explicit rates of convergence.
Thursday, September 17th
Peter Forrester , University of Melbourne
"Asymptotics of spacing distributions in RMT"
Time: 12:00 PM
Location: Hill 705
Abstract:
Spacing distributions between neighboring eigenvalues are a primary observable quantity in random matrix theory. More than 50 years ago F.J. Dyson introduced a log-gas heuristic which predicted their asymptotic forms. I'll discuss subsequent developments on this topic, including my recent joint work with J.L. Lebowitz relating on local limit theorems.
THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM.
Thursday, September 10th
Elliot Lieb , Princeton University
"Entropy and Entanglement Bounds for Reduced Density Matrices of Fermionic states"
Time: 2:00 PM
Location: Hill 705
Abstract: One of the important aspects of many-body quantum mechanics of electrons is the analysis of two-body density matrices. While the characterization of one-body density matrices is well known and simple to state, that of two-body matrices is far from simple -- indeed, it is not fully known. In this talk I will present joint work with Eric Carlen in which we study the possible entropy of such matrices. We find, inter alia, that minimum entropy is achieved for Slater determinant N-body parent functions.
Thus, from the entropic point of view, Slater determinants play the same role as condensates play for bosons.
Thursday, September 10th
Jozsef Beck , Rutgers University
"Many-particle dynamical systems"
Time: 12:00 PM
Location: Hill 705
Abstract: In the summer I finished two books about large dynamical systems. The (temporary) title of the first book is ``Many-particle dynamical systems, intrinsic entropy and the Second Law". The (temporary) title of the second book is ``Realistic ergodic theorems and large dynamical systems". I will give a short preview of the two books.
THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM!
Thursday, September 3rd
Ian Jauslin, University of Rome
" Non-perturbative renormalization group in a hierarchical Kondo model"
Time: 12:00 PM
Location: Hill 705
Abstract: In this seminar, a hierarchical version of the Kondo model is introduced and shown to be exactly solvable via renormalization
group techniques. The qualitative behavior of the magnetic susceptibility of the system is shown to be governed by a
non-trivial fixed point in the renormalization group flow.
The hierarchical Kondo model therefore provides an example of a system that can be studied exactly using
renormalization group methods without being asymptotically free.
The work presented here was carried out in collaboration with Giuseppe Benfatto and Giovanni Gallavotti.
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