International Conference

SOLID MATH 2018  

Mathematical and numerical methods for solid-state physics

McGill, Montreal   -  August 1- August 3, 2018

A satellite conference on the occasion

of the XIX International Congress on Mathematical Physics

Scientific Committee:

Eric Cances                                              (École des Ponts & INRIA, Paris)

Horia Cornean                                          (Aalborg University, Denmark)

Gianfausto Dell'Antonio     (SISSA, Trieste;  Emeritus at “Sapienza” University of Rome, Italy)

Vojkan Jakšić                                           (Mc Gill University, Montreal, Canada)

Arne Jensen                                             (Aalborg University, Denmark)

Gianluca Panati                                        (“Sapienza” University of Rome, Italy)

Organising Committee:

Eric Cances, Horia Cornean, Vojkan Jakšić, Gianluca Panati

Description of the event and of scientific scope:

Recent discoveries in solid-state physics are challenging the mathematical physics community, striving for an ambitious goal: a mathematical understanding – based on fundamental models – of a variety of new phenomena, ranging from the anomalous transport in aperiodic solids, to the striking conductivity properties of graphene and Weyl semimetals, to the emergence of topologically-ordered phases of macroscopic matter. The pioneering investigations in these fields require the interplay of different mathematical techniques (including operator theory, C*-algebras, differential and non-commutative geometry, K-theory) and a close confrontation with numerical simulations and experiments.

In view of that, we are planning a focused international conference, with a threefold aim:

(a)  to encourage the exchange of ideas and methods between active researchers in the field;

(b)  to disseminate the recent results and techniques, making them accessible, by informal talks, to Ph. D. students and young post-doc fellows;  

(c)   to communicate recent mathematical advances to the theoretical physics community.

Following the tradition of the first and second edition (Solid Math 2014, Trieste, Italy; Solid Math 2016, Aalborg, Denmark), we will focus on mathematical and numerical methods for solid-state physics, which is in our view a proper subset of condensed-matter physics, the latter including other topics as the theory of cold gases, quantum liquids and strongly correlated electrons.

As a main step forward with respect to the previous editions, the workshop will also cover the topic of numerical methods for computing electronic properties of solids. In the past decade, the range of applicability of first-principle simulation methods based on Density Functional Theory (DFT) and Green function methods (GW, Bethe-Salpeter equation) has dramatically increased. It is now possible to compute ab initio a large part of the phase diagram of a crystalline material, the diffusion rate of a vacancy in a crystal, the band gap of a semiconductor, or its absorption spectrum as a function of the temperature. However, many challenging problems remain, as for instance the first-principle simulation of solids with correlated electrons, of shallow point defects, of extended defects (dislocations, grain boundaries), and more generally of strongly disordered systems. Another interesting question at the interface of mathematical physics and scientific computing is the design of discretization methods and numerical algorithms compatible with some algebraic structure (e.g. the C*-algebra associated with a model of aperiodic solid), or some topological or geometrical properties (e.g. smooth Bloch bundles).

Joint effort from the mathematics, physics and scientific computing communities is needed to address these very difficult problems. Without any claim of completeness, in the 2018 conference we will focus on the following topics:

1. Adiabatic and time dependent methods in solid-state physics

2. C*-algebraic approach to quantum transport

3. Topological aspects of quantum transport (Quantum Hall effect, Quantum Spin Hall effect)

4. Magnetic Schrödinger operators

5. Localization of electrons in solids, including localization of Wannier functions

6. Mathematical results on Density Functional Theory (DFT) and Green function methods

7. Non linear Schrödinger equations and effective models for superconductivity

Targeted audience:

The list of speakers, to be decided about 8-9 months in advance, will include some of the most active researchers in the field of the mathematical methods for solid state physics. Therefore, we expect participants both from the mathematical physics and from the theoretical and computational solid-state physics community.  To stimulate a fruitful exchange of ideas and methods between the two communities, some research leaders in solid-state physics will be invited as keynote speakers.

Participation of Ph.D. students and young post-doc fellows will be encouraged by planning additional financial support for young participants and an adequate number of Junior Talks, namely shorter talks devoted to promising young people.