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

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