The University of Geneva and the EPF Lausanne invite you to the Journée Georges de Rham 2020 which will take place at the University of Geneva, Uni Bastions building, in the B106 auditorium (Olivier Reverdin).

The Journée Georges de Rham has been introduced in 1991 by the *Troisième cycle romand de mathématiques*. It convenes mathematicians not only of the CUSO universities, but also from the whole of Switzerland and from abroad and stimulates interaction between professors, postdocs and PhD students. Every year, the organisers invite two speakers of international reputation who present their vision of contemporary mathematics and of future developments. A particular aim is to offer doctoral students a modern high class perspective of mathematical sciences and to establish contacts on an international level and with other research groups.

This year, the invited speakers are **James Maynard** (University of Oxford) and **Alessio Figalli** (ETH Zurich).

**Conference subjects:**

__Alessio Figalli (ETH Zurich)__: *Regularity of interfaces in phase transitions via obstacle problems*

The so-called Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase change, for example ice melting to water. An important goal is to describe the structure of the interface separating the two phases. In its stationary version, the Stefan problem can be reduced to the classical obstacle problem, which consists in finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. The aim of this talk is to give a general overview of the classical theory of the obstacle problem, and then discuss recent developments on the structure of interfaces, both in the static and the parabolic settings.

__James Maynard (University of Oxford)__: *Approximating reals numbers by fractions*

How well can you approximate real numbers by fractions with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard - we don’t even know whether e+pi is rational or not!

If you allow for a tiny number of bad exceptions, then a beautiful dichotomy occurs - either almost everything can be approximated or almost nothing! I’ll talk about this problem and recent joint work with Dimitris Koukoulopoulos which classifies when these options occur, answering an old question of Duffin and Schaeffer. This relies on a fun blend of different ideas, including ergodic theory, analytic number theory and graph theory.

**Conference Schedule**:

16:15-17:15: **James Maynard**, *Approximating reals numbers by fractions*

17:15-17:45: Coffee Break

17:45-18:45: **Alessio Figalli**, *Regularity of interfaces in phase transitions via obstacle problems*

18:45-19:30: Reception

**Venue Information:**

*Arrival by train (Geneva main Station "Gare Cornavin")*

Take either tram n°15 (direction: Palettes) or n°18 (direction: Lancy-Bachet-Gare)

Get out at the tram stop "Plainpalais"

The building "Uni Bastions" is at about 5 min. walk

*Arrival by car*

The parking "Plaine de Plainpalais" is available near the building "Uni Bastions".

The entrance is accessible from:

Boulevard Georges-Favon 46

1205, Genève