Events Archive

Math Physics Seminar, Nicolas Rougerie, "Structure of large bosonic systems: the mean-field approximation and the quantum de Finetti theorem"
Tue, Nov 12, 2013, 4:30 pm5:00 pm
I will discuss a general strategy to derive Hartree's theory for the ground state of a generic interacting many-bosons system with mean-field scaling. The validity of the mean-field approximation is interpreted as a consequence of the structure of the set of bosonic density matrices with large number of particles, in particular of the so-called…
Math Physics Seminar, Yoshiko Ogata, "The Quantum Shannon-McMillan theorem and rank of spectral projections of macroscopic observables"
Tue, Oct 15, 2013, 4:30 pm5:30 pm
The classical Shannon-McMillan theorem states that an ergodic system has typical sets satisfying the asymptotic equipartition property. This theorem demonstrates the significance of entropy which gives the size of the typical sets. There has recently been great progress in the quantum version of the Shannon-McMillan theorem .In particular,…
Math Physics Seminar, Ajay Chandran, "Construction and Analysis of a hierarchical massless QFT"
Tue, Oct 1, 2013, 4:30 pm6:00 pm
l also show how methods from statistical mechanics can be used to prove the full scale invariance of this QFT. (Joint work with Abdelmalek Abdesselam and Gianluca Guadagni.)

Math Physics Seminar, Alessandro Giuliani, University of Rome, Striped states at the ferromagnetic transition
Tue, May 7, 2013, 4:30 pm6:00 pm
We consider a two-dimensional Ising model with nearest neighbor ferromagnetic and long-range, power-law decaying, antiferromagnetic interactions. We assume that the decay exponent of the antiferromagnetic part is larger than 4. The ground state displays a transition as the strength of the ferromagnetic interaction J is increased: if J is smaller…
Math Physics Seminar, Hugo Duminil, U of Geneva, Parafermionic observables in planar Potts models and Self Avoiding Walks
Tue, Apr 30, 2013, 4:30 pm6:00 pm
In this talk, we will discuss the role of parafermionic observables in the study of several planar statistical physics models. These objects have been introduced recently by Smirnov and Cardy and have been instrumental in Smirnov's proof of conformal invariance of the Ising model. We will explain how they can be combined with combinatorial and…
Math Physics Seminar - Vieri Mastropietro, Univ of Milan, Italy, Universal finite size corrections and the central charge in non solvable Ising models
Tue, Apr 16, 2013, 4:30 pm6:00 pm
We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal. The corresponding…
Mathematical Physics Seminar - Ron Peled, Tel Aviv University - Surface depinning under the two-dimensional hammock potential
Tue, Apr 2, 2013, 4:30 pm6:00 pm
We consider a random two-dimensional surface satisfying a Lipschitz constraint. The surface is uniformly chosen from the set of all real-valued Lipschitz functions on a two-dimensional discrete torus. Our main result is that the surface delocalizes, having fluctuations whose variance is at least logarithmic in the size of the torus. Our technique…
Mathematical Physics Seminar - Antti Knowles, Courant Institute - Quantum diffusion and delocalization for random band matrices
Tue, Mar 5, 2013, 4:30 pm6:00 pm
I give a summary of recent progress in establishing the diffusion approximation for random band matrices. We obtain a rigorous derivation of the diffusion profile in the regime W > N^{4/5}, where W is the band width and N the dimension of the matrix. As a corollary, we prove complete delocalization of the eigenvectors. Our proof is based on a new…
Cancelled: Math Physics Seminar - Jakob Yngvason, University of Vienna - Interacting Bosons in a Random Potential
Tue, Feb 26, 2013, 4:30 pm6:00 pm
We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential, but the character of the wave function of the condensate depends in an essential way on the interplay…
Math Physics Seminar - Frank Hansen, Tohoku University - Quantum Information Functionals
Tue, Feb 19, 2013, 4:30 pm6:00 pm
Quantum information functionals and their algebraic properties play an important role in quantum information theory. Recent developments in the theory of operator monotone and operator convex functions and related topics have simplified earlier results and also led to new insights. One example is the convexity of chi-square divergences. We…
CANCELLED Math Physics Seminar - Vojkan Jaksic, McGill University - Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Tue, Feb 12, 2013, 4:30 pm6:00 pm
Since the days of Chernoff, the hypothesis testing has played an important role in theoretical and applied statistics. In the last decade, the mathematical structure and basic results of classical hypothesis testing have been extended to the non-commutative setting and are an important branch of quantum information theory. It was recently…
High Energy Theory Seminar - IAS - Kevin Costello, Northwestern University - “Yangians and Supersymmetric Gauge Theory”
Mon, Feb 4, 2013, 2:30 pm4:00 pm
I'll describe a new link between supersymmetric gauge theories, with gauge group G, and the Yangian for the Lie algebra of G. The main result is that a certain twisted, deformed N=1 supersymmetric gauge theory, with gauge group G, is "controlled" by the Yangian built from G, in the same way that Chern-Simons theory is controlled by the quantum…
Math Phys Seminar: Jean-Pierre Eckman (University of Geneva) 'Atoms, Nuclei, and 3d Triangulations'
Tue, Dec 11, 2012, 3:30 pm5:00 pm
Based on the work of Durhuus-Jonsson and Benedetti-Ziegler, we revisit the question of the number of triangulations of the 3-ball. We introduce a notion of nucleus (a triangulation of the 3-ball without internal nodes, and with each internal face having at most 1 external edge). We show that every triangulation can be built from trees of…
Math Phys Seminar: Sylvia Serfaty (Université Pierre et Marie Curie - Paris 6 and Courant Institute) 'Towards crystallization in Coulomb systems'
Tue, Nov 13, 2012, 3:30 pm5:00 pm
We are interested in the statistical mechanics of (classical) two-dimensional Coulomb gases and one-dimensional log gases in a confining potential. We connect the Hamiltonian to the "renormalized energy", a way to compute the total Coulomb interaction of an infinite jellium, and whose minimum is expected to be achieved by the triangular lattice…
Math Phys Seminar: Jeffrey Schenker (IAS) 'Diffusion of wave packets for the Markov Schroedinger equation'
Thu, Mar 29, 2012, 3:00 pm4:30 pm
The long time evolution of waves in a homogeneous random environment will be discussed. Proving that the wave amplitude evolves diffusively over any sufficiently long time scales remains an open problem. One obstacle that arises is recurrence -- return of portions of the wave packet to regions previously visited. However, if one removes…
Math Phys Seminar: Sourav Chatterjee (Courant Inst. NYU) 'Invariant measures and the soliton resolution conjecture'
Tue, Mar 27, 2012, 3:30 pm5:00 pm
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution…
Math Phys Seminar: Christian Hainzl (University of Tuebingen) 'Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs'
Tue, Feb 28, 2012, 3:30 pm5:00 pm
We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs. This is joint work with Robert Seiringer.
Math Phys Seminar: Jonathan Breuer (Hebrew University) 'Nonintersecting random walkers with a staircase initial condition'
Tue, Feb 7, 2012, 4:30 pm6:00 pm
We study a model of one dimensional particles, performing geometrically weighted random walks that are conditioned not to intersect. The walkers start at equidistant points and end at consecutive integers. A naturally associated tiling model can be viewed as one of placing boxes on a staircase. For a particular value of the parameters we obtain a…
Math Phys Seminar: Ivan Corwin (Courant Inst. NYU) 'Macdonald Processes and Some Applications in Probability and Integrable Systems'
Tue, Nov 29, 2011, 4:30 pm6:00 pm
Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two parameters q, t in [0,1). Utilizing the Macdonald difference operators we prove several results about observables these processes, including Fredholm determinant formulas for q…