Events Archive

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.

In this talk I will give an overview of recent progress regarding mathematical questions and proofs of the spectral properties of Haldane pseudo-potentials.

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.

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 look elsewhere for a topological space.

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.

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.

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.

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.

PLEASE NOTE THIS TALK FROM 10/8 HAS BEEN RESCHEDLED TO 10/22/2019 -- THANK YOU!