Fisher-Hartwig asymptotics, Szego expansions, and applications to statistical physics

March 27 to March 31, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

Hajo Leschke, Alexander V. Sobolev, and Wolfgang Spitzer

Original Announcement

This workshop will focus on the theory of Toeplitz matrices (TM) and Wiener-Hopf operators (WHO).

In the recent ten or so years, the theory of these operators (TM and WHO) attracted a great deal of renewed attention from mathematical and theoretical physics communities due to the mathematical beauty of problems involved, and due to new applications in physics. For example, novel developments in quantum information theory and statistical physics concern the asymptotics of the (quantum) entanglement entropy of thermal equilibrium states, the overlap of ground states in the Anderson orthogonality catastrophe and the emptiness formation probability in quantum spin models. These quantities can be deduced from suitable Szego limit theorems, that is, from asymptotic results for traces of certain functions of TM and WHO.

The workshop will focus on the following problems.

The purpose of this workshop is to bring together experts from mathematics and theoretical/mathematical physics in order to address the topics outlined above, and to identify new directions in the field Szego expansions, stimulated by recent developments in both fields.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Double-scaling limits of Toeplitz determinants and Fisher–Hartwig singularities
by  Jani A. Virtanen
Fredholm Toeplitz operators with VMO symbols and the duality of generalized Fock spaces with small exponents
by  Zhangjian Hu and Jani A. Virtanen ,  Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Full Szego-type trace asymptotics for ergodic operators on large boxes
by  Adrian Dietlein
Loops in SL(2,C) and Factorization
by  Estelle Basor, and Doug Pickrell
Complex groups and root subgroup factorization
by  Doug Pickrell
Fredkin Spin Chain
by  Olof Salberger, and Vladimir Korepin