Learning from Insulators: New Trends in the Study of Conductivity of Metals

The purpose of this workshop is to promote a large-scale collaboration across different fields of mathematical physics in order to systematically investigate electronic transport in metals. In order to do this, we will draw inspiration on recent progress made in the area of topological insulators, interacting systems and disordered systems.

Since we aim to bring together a broad and diverse community of specialists in these fields, previous to the workshop there will be mini-courses on

• Classical mechanics and transport
• Semiclassical methods for electronic transport
• Algebraic methods for interacting systems
• Disordered quantum systems

These courses will lay the ground and common language for the discussions that will take place during the week of the workshop.

During the workshop, talks and group discussions will be structured around the following areas: classical mechanics, functional analysis, semiclassical analysis, probability theory, topology and noncommutative geometry. We aim at addressing the following questions, inspired by Lifshitz’s approach to the study of conductivity in metals using semiclassical equations of motion:

• A refinement of Lifshitz equations of motions as an approach to study conductivity and the study  of fate of the Fermi surface in presence of perturbations;
• Derivation of a semiclassical theory that includes subleading corrections and topological terms and takes into account external fields;
• A fully quantum mechanical description that allows to consider disorder and many-body effects. 

Recordings of the talks are available via Youtube playlist:  https://www.youtube.com/playlist?list=PLJJSqTiwN2ZX82Ky-kK3Ke62-f9MOvDP6

In this workshop, we will welcome researchers on the global geometry of integrable systems, both from the point of view of differential geometry and algebraic topology, experts in semiclassical theory from the point of view of integrable systems and magnetic pseudodifferential theory, and experts in disordered and many-body quantum systems, working in both the noncommutative operator algebraic setting and on random Schrödinger operators.

There will be panoramic talks and more specialized talks, followed by open exchanges.
Prior to the workshop we will collect questions or remarks from the participants, with the purpose to kickstart discussions.

We expect that these activities, together with the broad expertises of the participants will allow for a fruitful exchange of ideas and for a fresh take at an old topic, bringing recent advances in the study of insulators to the study of metals.

By the end of the week we expect to have a document summarising future directions for research by collecting interesting questions and observations arisen during the workshop and relevant references.