Events Archive

Mathematical Physics Seminar, Tues Mar 29, 4:30PM, Jadwin A06, Vieri Mastropietro, IAS and University of Milan, "Anomaly non-renormalization on a lattice"
Tue, Mar 29, 2022, 4:30 pm4:30 pm

The Adler-Bardeen non-renormalization is a basic property of anomalies with important physical implications, ranging from particle physics to condensed matter. We prove its validity in lattice models at a non-perturbative level, focusing in particular on fermion-vector boson models in 3+1 and 1+1 dimensions. The proof relies on regularity…

Mathematical Physics Seminar, Tues Mar 22, 4:30pm, Jadwin A06, Louis-Pierre Arguin, Baruch College & Graduate Center CUNY``Statistical mechanics perspective on the large values of the Riemann zeta function’’
Tue, Mar 22, 2022, 4:30 pm4:30 pm

I will give an account of the recent progress in probability and in number theory to understand the large values of the zeta function on the critical line, especially in short intervals. The problems have interesting connections to statistical mechanics of disordered systems, both in their interpretations…

Mathematical Physics Seminar, Tues Mar 15, 4:30pm, Jadwin A06, Amol Aggarwal, IAS, Princeton,"Six-Vertex Model and the KPZ Universality Class "
Tue, Mar 15, 2022, 4:30 pm4:30 pm

In this talk we explain recent results relating the six-vertex model and the Kardar-Parisi-Zhang (KPZ) universality class. In particular, we describe how the six-vertex model can be used to analyze stochastic interacting particle systems, such as asymmetric exclusion processes, and how infinite-volume pure…

Mathematical Physics Seminar, Tues, Nov 30, 4:30 pm, Jadwin A-06, Simone Warzel, TU-Munich, “The Spectral Gap in Fractional Hall Systems”
Tue, Nov 30, 2021, 4:30 pm4:30 pm

In this talk I will give an overview of recent progress regarding mathematical questions and proofs of the spectral properties of Haldane pseudo-potentials. These are short range interactions projected onto the lowest Landau level and are tailored to model properties of fractional Hall fluids and their…

Mathematical Physics Seminar, Tue Nov. 9, 4:30 p.m. Jadwin A-06 - Simon Becker, Courant Institute, "Mathematical Properties of Twisted Bilayer Graphene"
Tue, Nov 9, 2021, 4:30 pm4:30 pm

Twistronics is the study of how the angle (the twist) between layers of two-dimensional materials can change their electronic structure. When two sheets of graphene are twisted by those angles the resulting material exhibits flat bands which, as argued in the physics literature, is related to…

Mathematical Physics Seminar, Tues, Nov 2, 4:30pm, Jadwin A06, Jacob Shapiro, Princeton University, “Depinning in the integer-valued Gaussian field and the BKT phase of the 2D Villain model”
Tue, Nov 2, 2021, 4:30 pm4:30 pm

It is shown that the Villain model of two-component spins over two dimensional lattices exhibits slow, non-summable, decay of correlations at any temperature at which the dual integer-valued Gaussian field exhibits depinning. For the latter, we extend the recent proof by Lammers of the existence of a…

The Universe from a single Particle - Michael Freedman - Microsoft Q
Mon, Nov 1, 2021, 4:30 pm4:30 pm

I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) - can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108…

Mathematical Physics Seminar, Tues, Oct 26, 4:30pm, Jadwin A06, Terry Loring, University of New Mexico, “EMERGENT TOPOLOGY FROM FINITE VOLUME TOPOLOGICAL INSULATORS”
Tue, Oct 26, 2021, 4:30 pm4:30 pm

Finite volume (or area) models for topological insulators are closer to experiment than in_nite volume models. However, they are only indirectly connected to Brillouin zone and so we need to…

Mathematical Physics Seminar, Tue, Oct 12, 4:30pm Jadwin A-06, Giorgio Cipolloni, PCTS, "Extension of Wigner's Vision to Quantum Chaos"
Tue, Oct 12, 2021, 4:30 pm4:30 pm

After reviewing recent progress in random Hermitian and non-Hermitian matrix theory, we prove that eigenvectors of Wigner matrices satisfy the Eigenstate Thermalisation Hypothesis (ETH), which is a strong form of Quantum Unique ergodicity (QUE) with optimal speed of convergence. This requires proving certain…

Mathematical Physics Seminar: Simone Warzel,TU-Munich, "Spectral Gaps, Incompressibility and Fragmented Matrix-Product State in a Fractional Quantum Hall System"
Tue, May 5, 2020, 2:00 pm2:00 pm

In the thin cylinder regime Haldane’s pseudo-potential corresponding to one-third filling results in a frustration-free fermionic lattice Hamiltonian which is dipole-conserving with an added electrostatic interaction. Its zero-energy eigenspace is exponentially large. Nevertheless, it admits a a rather simple, full description in terms of a…

Mathematical Physics Seminar: Uzy Smilansky, Weizmann Institute, "Systematics of spectral shifts in random matrix ensembles"
Fri, May 1, 2020, 11:00 am11:00 am

We chose a $N\times N$ Hermitian matrix randomly picked from one of the  random Gaussian matrix ensembles $(\beta =1,2,4)$ - the reference matrix. Perturbing it with a sequence of rank $t$ matrices, with $t$ taking the values $1\le t \le N$, we study the expected difference between the spectra of the  perturbed and the reference matrices as a…

Mathematical Physics Seminar: Marius Lemm, Harvard University, "Spectral Gaps in Quantum Spin Systems"
Tue, Mar 10, 2020, 4:30 pm4:30 pm

Quantum spin systems are many-body models which are of wide interest in modern physics and at the same time amenable to rigorous mathematical analysis. A central question about a quantum spin system is whether its Hamiltonian exhibits a spectral gap above the ground state. The existence of such a spectral gap has far-reaching consequences, e.g…

Mathematical Physics Seminar: Ian Jauslin, Princeton University, "A Simplified Approach to Interacting Bose Gases"
Tue, Mar 3, 2020, 4:30 pm4:30 pm

I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the '63 effective theory…

Mathematical Physics Seminar: Michael Kiessling, Rutgers University, "Quantization of the electromagnetic field as a consequence of old-fashioned semi-relativistic quantum mechanics of radiating atoms''
Tue, Feb 25, 2020, 4:30 pm4:30 pm

Born's probabilistic interpretation of Schroedinger's wave function is shown to lead to a semi-relativistic quantum mechanics of atoms, molecules, etc., coupled with electromagnetic radiation. No second quantization is invoked, yet the photon naturally shows up in this formulation.

Mathematical Physics Seminar: Charles Newman, Courant Institute, "A Gaussian Process Related to the Mass Spectrum of the Near-Critical Ising Model"
Tue, Feb 11, 2020, 4:30 pm4:30 pm

The continuum scaling limit of the Ising model in d dimensions at the critical temperature whose magnetic field properly scales to zero with lattice spacing is (or should be) a non-Gaussian generalized random field Phi for d = 2 (and d = 3). This field is (or should be)  related to arelativistic quantum field theory with one time and d-1 space…

Math Physics Seminar | Paul Bourgade, NYU | "Branching processes in random matrix theory and analytic number theory" | Jadwin A06
Tue, Nov 12, 2019, 4:30 pm4:30 pm

Fyodorov, Hiary and Keating have conjectured that the maximum of the characteristic polynomial of random matrices behaves like extremes of log-correlated Gaussian fields. This allowed them to predict the size of local maxima of L-function along the critical axis. I will explain the origins of this conjecture and…

Math Physics | Martin Fraas, Virginia Tech | "A many-body Fredholm index for ground state spaces and Abelian anyons" | Jadwin A06
Tue, Oct 29, 2019, 4:30 pm4:30 pm

We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any charge-conserving system with a topologically ordered p-dimensional ground state sector. The index is fractional with the denominator given by p. In particular, this yields a new short proof of the…

Math Physics Seminar | Michael Aizenman, Princeton | ``Geometric analysis of frustration in a class of SU(2S+1) invariant quantum spin chains’’ | Jadwin A06
Tue, Oct 22, 2019, 4:30 pm4:30 pm


Unlike their classical counterparts, quantum antiferromagnetic systems exhibit ground state frustration effects even in one dimension.  A case in point is the SU(2S+1) invariant spin chain, with the interaction between pairs of neighboring S-spins given by…

Math Physics Seminar | Rodrigo Matos, Michigan State | "Localization in the Disordered Hubbard Model within Hartree-Fock Theory" | Jadwin A06
Tue, Oct 15, 2019, 4:30 pm4:30 pm

We aim at presenting a simple context where known results on Anderson localization for systems of non-interacting particles in a random environment may be extended to systems with weak interactions.

Using the fractional moment method it is shown that, within the Hartree-Fock…

Math Physics Seminar, | Simone Warzel, TU, Munich | "The Quantum Random Energy Model" | Jadwin A06
Tue, Sep 24, 2019, 4:30 pm4:30 pm

The quantum random energy model serves as a simple cornerstone, and a testing ground, for a number of fields.  It is the simplest of all mean-field spin glass models in which quantum effects due to the presence of a transversal field are studied.  Renewed interest in its spectral properties arose recently in…