The VI AMMCS International Conference

Waterloo, Ontario, Canada | August 14-18, 2023

AMMCS 2023 Plenary Talk

Partial Differential Equations of Quantum Mechanics

Israel Michael Sigal (University of Toronto)

In this talk I will describe key partial differential equations of quantum mechanics and condensed matter physics. I will review briefly the origins of the equations, their properties and some of the recent results. I will also touch upon some open problems. No preliminary knowledge of quantum mechanics is required. All needed concepts will be introduced in the talk.
Israel Michael Sigal is a University Professor at the University of Toronto where he also holds the Norman Stuart Robertson Chair in Applied Mathematics. He has made significant contributions to mathematical physics and applied mathematics. These include a proof, together with A. Soffer, of the asymptotic completeness of scattering for quantum many-body short-range systems; the development, with V. Bach and J. Fr ohlich, of the mathematical theory of quantum radiation in the non-relativistic regime (non-relativistic QED); the introduction, with V. Bach and J. Fr ohlich, of the operator renormalization group; and determination, jointly with S. Gustafson, Z. Gang, L. Jonsson, J. Fr ohlich and T. Tzaneteas, of dynamics of solitons, quantum vortices and vortex lattices. More recently, Sigal has been addressing mathematical questions of quantum information science, proving, jointly with J. Faupin and M. Lemm, the long-standing conjecture on existence of an effective light cone in the lattice Bose gases, and deriving, with Jingxuan Zhan, a large class of general constraints on the flow of quantum information in general lattice quantum many-body systems.

Sigal has published over 250 peer-reviewed papers and is co-author of books on spectral theory and on quantum mechanics. He is a Fellow of the AMS and a Fellow of the Royal Society of Canada. His research achievements have been recognized with numerous awards and lectureships, including the Killam Fellowship, the CRM/Fields Institute Prize, invited talks at the ICM and ICMP, and addresses at the AMS and CMS.