Events Archive

Mathematical Physics Seminar, Tues, Apr 2, 4:30pm, Jadwin A06, Patrick Lopatto, Brown University, "The Mobility Edge of Lévy Matrices"
Tue, Apr 2, 2024, 4:30 pm5:30 pm

Lévy matrices are symmetric random matrices whose entry distributions have power law tails and infinite variance. They are predicted to exhibit an Anderson-type phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the context for this conjecture, and describe a result…

Mathematical Physics Seminar, Tues, Mar 26, 4:30pm, Jadwin A06, Yu Deng, USCS, "Gibbs Measure Dynamics in Nonlinear Dispersive Equations"
Tue, Mar 26, 2024, 4:30 pm5:30 pm

The Phi^4, and generally Phi^p measures, which are extensively studied in quantum field theory, also occur naturally as invariant Gibbs measures for certain (dispersive) Hamiltonian PDEs and parabolic SPDEs. A fundamental question is to rigorously justify the invariance of such measures under said dynamics, which leads to deep questions in the…

Mathematical Physics Seminar, Tues, Mar 5, 4:30pm, Jadwin A06, Alexander B. Watson, University of Minnesota, "Multiple-Scales Perspective on Moiré Materials""
Tue, Mar 5, 2024, 4:30 pm5:30 pm

In recent years, experiments have shown that twisted bilayer graphene and other so-called ``moiré materials'' realize a variety of important strongly-correlated electronic phases, such as superconductivity and fractional quantum anomalous Hall states. I will present a rigorous multiple-scales analysis justifying the (single-particle) Bistritzer…

Mathematical Physics Seminar, Tues, Feb 27, 4:30pm, Jadwin A06, Ian Jauslin, Rutgers University, "A Criterion for Crystallization in Hard-Core Lattice Particle Systems"
Tue, Feb 27, 2024, 4:30 pm5:30 pm

As is well known, many materials freeze at low temperatures. Microscopically, this means that their molecules form a phase where there is long range order in their positions. Despite their ubiquity, proving that these freezing transitions occur in realistic microscopic models has been a significant challenge, and it remains an open problems in…

Mathematical Physics Seminar, Tues, Feb 20, 4:30pm, Jadwin A06, Gilles Parez, University of Montreal,"The Fate of Entanglement"
Tue, Feb 20, 2024, 4:30 pm5:30 pm

Entanglement is a fundamental property of quantum mechanics, and plays an increasing role in our understanding of many-body systems, in and out of equilibrium. In multipartite systems, different forms of entanglement can exist between various sets of particles, and its detection, even theoretical, remains an outstanding challenge. In this talk,…

Mathematical Physics Seminar, Tues, Feb 13, 4:30pm, PGI Open Space, Tom Stoiber, Yeshiva University, "Violations of Bulk-Edge Correspondence for Topological Insulators"
Tue, Feb 13, 2024, 4:30 pm5:30 pm

Bulk-edge correspondence is an important part of the theory of topological insulators which relates topological invariants in the bulk of an insulator to those of its topologically protected edge modes. Despite numerous rigorous proofs, this paradigm has recently been shown to fail in continuum models for topological phases where the…

Mathematical Physics Seminar, Tues, Feb 6, 4:30pm, PGI Open Space, Roland Bauerschmidt, Courant Institute of Mathematics, NYU, "The Polchinski Equation, Semiconvexity, and Stochastic Dynamics"
Tue, Feb 6, 2024, 4:30 pm5:30 pm

I will give an overview of a perspective on Polchinski's continuous formulation of the renormalization group, developed over the last few years with T. Bodineau and B. Dagallier, as well as some applications to functional inequalities and sample path regularity of Euclidean field theories.

Time permitting, I will also…

Mathematical Physics Seminar, Tues, Jan 30, 4:30pm, Jadwin A06, David Huse, Princeton University, "Many-body localization"
Tue, Jan 30, 2024, 4:30 pm5:30 pm

I will discuss some of the present conceptual and theoretical (but not mathematical) understanding of the many-body localized (MBL) phase and its instabilities.  In most cases, for the MBL phase to remain stable in the limit of an infinite system this limit needs to be taken differently from the standard thermodynamic limit (Gopalakrishnan…

Mathematical Physics Seminar, Tues, Nov 28, 4:30pm, Jadwin A07, Nikita Sopenko, IAS,"Anomalous Symmetries of Quantum Spin Chains and Generalization of Lieb-Schultz-Mattis Theorem"
Tue, Nov 28, 2023, 4:30 pm5:30 pm

I will discuss how symmetries of quantum spin systems can be realized. For a given realization of a symmetry group G of a 1d spin system, I will define the anomalous index that takes values in the cohomology H^4(BG) of the classifying space of the group. I will show that a G-invariant system with a non-trivial anomalous index can not have a…

Mathematical Physics Seminar, Tues, Nov 14, 4:30pm, Jadwin A07, Michael I. Weinstein, Columbia / Princeton / IAS,"Pseudo-magnetism and Landau Levels in Deformed Honeycomb Structures"
Tue, Nov 14, 2023, 4:30 pm5:30 pm

A non-uniform deformation of a honeycomb medium induces effective-magnetic and effective-electric fields. One may choose a deformation which gives rise to a constant perpendicular effective-magnetic field with Landau-level spectrum (flat bands). In the setting of photonic crystals, the tight binding model is generally not applicable. I’ll…

Mathematical Physics Seminar, Tues, Nov 7, 4:30pm, Jadwin A07, Lior Alon, MIT, "Positive Fourier Quasicrystals, One-Dimensional and Higher Dimensions"
Tue, Nov 7, 2023, 4:30 pm5:30 pm

The concept of "quasi-periodic" sets, functions, and measures is

prevalent in many fields including Mathematical Physics,

Fourier Analysis, and Number Theory. The Poisson summation formula provides a “Fourier characterization” for discrete periodic sets, saying that the Fourier transform of the counting measure of a discrete…

Mathematical Physics Seminar, Tues, Oct 31, 4:30pm, Jadwin A06, Mariya Shchenbina, Institute for Low Temperature Physics of National Ukrainian Ac. Sci. (Kharkiv) & IAS, Super Symmetry Approach to the Non Hermitian Random Matrices:Deformed Ginibre Ensemble
Tue, Oct 31, 2023, 4:30 pm5:30 pm

We consider a complex Ginibre ensemble of random matrices with a deformation $H=H_0+A$, where $H_0$ is a Gaussian complex Ginibre matrix and $A$ is a rather general deformation matrix. The analysis of such ensemble is motivated by many problems of random matrix theory and its applications. We use the Grassmann integration methods to obtain…

Mathematical Physics Seminar, Tues, Oct 24, 4:30pm, Jadwin A07, Bertrand Duplantier, Paris-Saclay University ,"Hamiltonian Paths on Bipartite Random Planar Maps and KPZ "
Tue, Oct 24, 2023, 4:30 pm5:30 pm

We consider various configuration exponents of Hamiltonian paths drawn on bipartite random planar maps. Estimates from exact enumerations are compared with predictions based on the KPZ relations, as applied to  exponents on the regular hexagonal lattice. Surprisingly, a naive use of KPZ does not reproduce all the measured exponents, but an…

Mathematical Physics Seminar, Tues, Oct 10, 4:30pm, Jadwin A06, Sourav Chatterjee, Stanford and IAS,"Spin Glass Phase in the Edwards-Anderson Model at ZeroTemperature"
Tue, Oct 10, 2023, 4:30 pm5:30 pm

While the analysis of mean-field spin glass models has seen tremendous progress in the last twenty years, lattice spin glasses have remained largely intractable. I will talk about recent progress on this topic, giving the first proof of glassy behavior in the Edwards-Anderson model of lattice spin glasses.

Mathematical Physics Seminar, Tues, Oct 3, 4:30pm, Jadwin A07, Jakob Bjornberg, University of Gothenburg, "Dimerisation in mirror models and quantum spin chains"
Tue, Oct 3, 2023, 4:30 pm5:30 pm

We consider two models of random loops where we prove breaking of translational symmetry. The first is a mirror model, where the loops are formed by light rays bouncing in a labyrinth of randomly oriented mirrors. The second is a probabilistic representation of a quantum spin chain, and can be obtained as a limit of the first, for inhomogeneous…

Mathematical Physics Seminar, Tues, Sep 26, 4:30pm, Jadwin A07, Margherita Disertori, University of Bonn,"Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model"
Tue, Sep 26, 2023, 4:30 pm5:30 pm

Localization/delocalization transition in random Schrödinger operators cannot in general be seen from the behavior of the corresponding Integrated Density of States (IDS). Here we consider a random Schrödinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model, and show that…

Mathematical Physics Seminar, Tues, Sept 19, 4:30pm, Jadwin A07, Oren Yakir, Tel-Aviv University, "Random Weierstrass zeta functions"
Tue, Sep 19, 2023, 4:30 pm5:30 pm

In electrostatic terminology, an electrical field of a stationary point process is a vector field whose distributional divergence is equal to the counting measure of the point process minus the Lebesgue measure. In the talk we will give a simple answer to the following question: when does a planar stationary point process generate a stationary…

Mathematical Physics Seminar, Tues, April 18, 4:30pm, Jadwin A06, Ian Jauslin, Rutgers University, "Non-perturbative Behavior of Interacting Bosons at Intermediate Densities"
Tue, Apr 18, 2023, 4:30 pm5:30 pm

Much attention has been given to systems of interacting Bosons in the dilute regime, where powerful theoretical tools such as Bogolyubov theory give detailed and accurate predictions. In this talk, I will discuss a different approach to studying the ground state of Boson systems, which Carlen, Lieb and I have recently found to be accurate at…

Mathematical Physics Seminar, Tues, April 11, 4:30pm, Jadwin A06, Dan Borgnia, UC Berkeley,"Projected Green's Function Methods Applied to Quasi-Periodic Systems and the Dry Ten Martini Problem"
Tue, Apr 11, 2023, 4:30 pm5:30 pm

The resolvents of finite volume restricted Hamiltonians, GxxΛ(⍵), have long been used to describe the localization of quantum systems. More recently, projected Green's functions (pGfs) -- finite volume restrictions of the resolvent -- have been applied to translation invariant free fermion systems, and the pGf zero eigenvalues have been shown…

Mathematical Physics Seminar, Tues, Mar 28, 4:30pm, Jadwin A06, Ron Peled, Tel Aviv University and IAS, "Minimal Surfaces in Random Environment"
Tue, Mar 28, 2023, 4:30 pm5:30 pm

A minimal surface in a random environment (MSRE) is a surface which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary values. Apart from their intrinsic interest, such surfaces are further motivated by connections with disordered spin systems and first-passage percolation models. We…