Events Archive

Math Physics Seminar, John Imbrie, U. of Virginia, "Rare Region Effects and Many-Body Localization" Jadwin 343
Tue, Oct 17, 2017, 4:30 pm4:30 pm

Abstract:  Certain strongly disordered many-body quantum systems are incapable of reaching thermal equilibrium. The nature of this so-called many-body localized (MBL) phase has recently been an active area of research. The phenomenon can be understood through perturbative approximations, but rare regions with weak disorder (Griffiths regions)…

Math Physics Seminar, Yinon Spinka, Tel Aviv U., "Macroscopic loops in the loop O(n) model" Jadwin 343
Tue, Oct 10, 2017, 4:30 pm4:30 pm


A loop configuration on the hexagonal (honeycomb) lattice is a finite subgraph of the lattice in which every vertex has degree 0 or 2, so that every connected component is isomorphic to a cycle. The loop O(n) model on the hexagonal lattice is a random loop configuration, with the energy of of a loop configuration taken to…

Math Physics Seminar, Yuval Peres, Microsoft Research, "Gravitational allocation to uniform points on the sphere " Jadwin 343
Tue, Oct 3, 2017, 4:30 pm5:30 pm


Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them ?    "Fairly" means that each region has the same area.   It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins…

Math Physics Seminar, Vincent Vargas, ENS, "Ward and Belavin-Polyakov-Zamolodchikov (BPZ) identities for Liouville quantum field theory on the Riemann
Tue, Nov 15, 2016, 4:30 pm5:30 pm
The foundations of modern conformal field theory (CFT) were introduced in a 1984 seminal paper by Belavin, Polyakov and Zamolodchikov (BPZ). Though the CFT formalism is widespread in the physics literature, it remains a challenge for mathematicians to make sense out of it. Liouville CFT (or quantum field theory), introduced by Polyakov in his…
Math Physics Seminar, Eviatar Procaccia, Texas A & M, "Can one hear the shape of a random walk?"
Tue, Oct 25, 2016, 4:30 pm5:30 pm
We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to…
Math Physics Seminar, Vieri Mastropietro, U. of Milano, "Localization of interacting fermions with quasi-random disorder"
Tue, Oct 18, 2016, 4:30 pm5:30 pm
We consider interacting electrons in a one dimensional lattice with an incommensurate Aubry-Andre' potential in the regime when the single-particle eigenstates are localized. We rigorously establish persistence of ground state localization in presence of weak many-body interaction.The proof uses a quantum many body extension of methods adopted…
Special Math Physics Seminar, Anna Vershynina, Basque Center, Spain, "Quantum analogues of geometric inequalities for Information theory"
Mon, Oct 17, 2016, 2:30 pm3:30 pm
Geometric inequalities, such as entropy power inequality or the isoperimetric inequality, relate geometric quantities, such as volumes and surface areas. Classically, these inequalities have useful applications for obtaining bounds on channel capacities, and deriving log-Sobolev inequalities. In my talk I provide quantum analogues of certain well…
Special Math Physics Seminar, Alessandro Giuliani, U. of Rome 3, "Universality of transport coefficients in the Haldane-Hubbard model"
Wed, Oct 12, 2016, 4:30 pm5:30 pm
In this talk I will review some selected aspects of the theory of interacting electrons on the honeycomb lattice, with special emphasis on the Haldane-Hubbard model: this is a model for interacting electrons on the hexagonal lattice, in the presence of nearest and next-to-nearest neighbor hopping, as well as of a transverse dipolar magnetic field…
Special Math Physics Seminar, Marcello Porta, Zurich U., "Mean field evolution of fermonic systems"
Wed, Oct 5, 2016, 2:00 pm3:00 pm
In this talk I will discuss the dynamics of interacting fermionic systems in the mean field regime. Compared to the bosonic case, fermionic mean field scaling is naturally coupled with a semiclassical scaling, making the analysis more involved. As the number of particles grows, the quantum evolution of the system is expected to be effectively…
Math Physics Seminar, Eliran Subag, Weizmann, "Critical points and the Gibbs measure of a spherical spin glass model"
Tue, Sep 27, 2016, 4:30 pm5:30 pm
For integers N let H_N(x) be an isotropic Gaussian field on the N-dimensional unit sphere, meaning that Cov(H_N(x),H_N(y)) is a function, f_N, of the inner product of . The spherical spin glass models of statistical mechanics are such random fields, with f_N = N f with the function independent of the dimension N. The intricate landscape…
Math Physics Seminar, Roderich Tumulka, Rutgers U., "Probability Distribution of the Time at Which an Ideal Detector Clicks"
Tue, Apr 26, 2016, 4:30 pm5:30 pm
We consider a non-relativistic quantum particle surrounded by a detecting surface and ask how to compute, from the particle's initial wave function, the probability distribution of the time and place at which the particle gets detected. In principle, quantum mechanics makes a prediction for this distribution by solving the Schrodinger equation of…
Math Physics Seminar, Phil Sosoe, Harvard, "Sharp quasi-invariance for the 4th order nonlinear Schroedinger equation"
Tue, Apr 19, 2016, 4:30 pm5:30 pm
Starting with the work of Lebowitz-Rose-Speer in 1988, there has been great interest and significant progress in establishing invariance of certain Gibbs-type measures with respect to dispersive equations in 1 and 2 dimensions. The invariant measures in question are absolutely continuous with respect to the free field, and thus concentrated…
Math Physics Seminar, Juerg Froehlich, ETH, Zurich, "Physical implications of the chiral anomaly -"
Tue, Apr 5, 2016, 4:30 pm5:30 pm
Starting with an analysis of chiral edge currents in 2D electron gases exhibiting the quantum Hall effect I will discuss the role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly broken parity and time-reversal and in time-reversal-invariant 2D topological insulators exhibiting edge spin-currents. I will…
Math Physics Seminar, David Brydges, U of British Columbia, "The lace expansion for $\phi^{4}$"
Tue, Mar 29, 2016, 4:30 pm5:30 pm
The lace expansion provides a formula for the two point function which has been useful for critical percolation, self-avoiding walk and related problems in high dimensions. Recently Akira Sakai has shown that the Ising model and the one component $\phi^4$ model admit similar formulas. I will review the basic features of the lace expansion…
Math Physics Seminar, Robin Reuvers, U of Copenhagen, "The Bogoliubov free energy functional"
Tue, Mar 22, 2016, 4:30 pm5:30 pm
Einstein's classic treatment of Bose-Einstein condensation for non-interacting bosons predicts at what temperature the phase transition to BEC occurs, but how this critical temperature changes when the bosons start to interact weakly is an old problem, first posed by Feynman in 1953. In this talk, I will address this question in a variational…
Math Physics Seminar, Michael Brenner, Harvard, "A Potential mechanism for a singular solution of the Euler Equation"
Tue, Mar 1, 2016, 4:30 pm5:30 pm
I will describe a potential mechanism for a singular solution of the Euler equation. The mechanism involves the interaction of vortex filaments, but occurs sufficiently quickly and at a small enough scales that could have plausibly evaded experimental and computational detection. Joint work with Sahand Hormoz and Alain Pumir.

Math Physics Seminar, Lukas W. Schimmer, Princeton, "Asymptotics of the eigenvalues of operators for mirror curves"
Tue, Feb 23, 2016, 4:30 pm5:30 pm
Using the coherent state transform I willI establish the asymptotical behaviour of the Riesz mean for functional-difference operators associated to mirror curves of special del Pezzo Calabi–Yau threefolds. Furthermore, I will prove the Weyl law for the eigenvalue counting function of these operators, therefore implying that their inverses are…
Math Physics Seminar, Simone Warzel, TU, Munich, "Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas"
Tue, Feb 16, 2016, 4:30 pm5:30 pm
Understanding the various aspects, and even the qualitative structure of phase diagrams of interacting many-body systems in the presence of static disorder still poses a big challenge. In this context, and in view of the woefully short list of rigorous results on disordered systems with interaction, limiting or integrable model systems present a…
Math Physics Seminar, Roland Bauerschmidt, Harvard, "Local eigenvalue statistics for random regular graphs"
Tue, Nov 10, 2015, 4:30 pm6:00 pm
I will discuss results on local eigenvalue statistics for uniform random regular graphs. Under mild growth assumptions on the degree, we prove that the local semicircle law holds at the optimal scale, and that the bulk eigenvalue statistics (gap statistics and averaged energy correlation functions) are given by those of the GOE. Joint work with…
Math Physics Seminar, Bertrand Duplantier, Ins. Phys. Théorique, Saclay, "Schramm -- Loewner Evolution and Liouville Quantum Multifractality"
Tue, Oct 27, 2015, 4:30 pm5:30 pm
We describe some recent advances in the study of the fundamental coupling of a canonical model of random paths, the Schramm--Loewner Evolution (SLE), to a canonical model of random surfaces, Liouville Quantum Gravity (LQG). The latter is expected to be the conformally invariant continuum limit of various models of random planar maps. Via the…