ICM 2018 Satellite Conference:

Topics in Mathematical Physics

July 26-31, 2018

Institute of Mathematics and Statistics University of São Paulo

Institute of Physics-University of São Paulo

Brief abstract of the Conference

Theme and Topics

The aim the satellite conference is to establish fruitful connections between Ergodic Theory, new probabilistic and algebraic approaches in Mathematical Physics. The meeting will allow emerging leaders in the domain to showcase their research and to interact with established scientists. The research fields are divided into three topics:


Gibbs-non-Gibbs issues: The behavior of Gibbs measures, under transformations (do they remain Gibbsian or not?), and the properties of related notions of regularity, originating from connected fields has been a fruitful topic of research. Recent issues which have seen advances in our understanding are the relation between Gibbs measures and g-measures, -it turned out that neither of these classes includes each other-, the behavior of Gibbs measures under discretization, which has led a to solution of longstanding question of Liggett in Interacting Particle Systems, showing a non-ergodic system with a unique invariant measure, and the behavior of Gibbs measures under evolutions including delay terms.

Organizers: Aernout van Enter (University of Groningen, the Netherlands)
            Wioletta Ruszel (TU Delft, the Netherlands)

Complex Networks

Organizers: Frank den Hollander (Leiden University, the Netherlands)
            Luca Avena (Leiden University, the Netherlands)

Mathematical Aspects of Quantum Physics

This section focusses on new developments in the algebraic approaches to physical systems describing non-relativistic quantum particles, atoms and molecules. These (non-commutative) approaches are reminiscent of probability theory with the study of critical phenomena (phase transitions, percolation, multi-scale analysis). Functional analysis also plays a central role in this research field. In addition to its eminent position in traditional mathematical and theoretical physics, this branch of research is increasingly important in various domains of modern science, including quantum computing and quantum chemistry.

Organizers: João C. A. Barata (USP, Brazil)
            Walter de Siqueira Pedra (USP, Brazil)
            Sébastien Breteaux (Université de Lorraine, France)
            Jean-Bernard Bru (University of the Basque Country & BCAM, Basque Country)

Ergodic Theory and Thermodynamic Formalism

After the fundamental contributions of Bowen, Ruelle, Sinai and many others, the research on topics about thermodynamic formalism became an important branch of ergodic theory and dynamical systems. This section will focus on results about pressure (free energy), Gibbs states, equilibrium states, phase transitions, ground states and large deviations from an ergodic and dynamic point of view.

Organizers: Rodrigo Bissacot (USP, Brazil)
            Eduardo Garibaldi (UNICAMP, Brazil)
            Artur Oscar Lopes (UFRGS, Brazil)
            Philippe Thieullen (Université de Bordeaux, France)