Conferências Magnas - Wendelin Werner

Wendelin Werner
Professor da Université Paris-Sud 11 in Orsay


3 de maio
Universidade Federal de Minas Gerais às 10 horas
Título: Surface fluctuations and their geometries

Drawing at random in the plane

Abstract: We will give a heuristic overview of recent mathematical results that deal with the general question of how to draw “naturally” and at random curves or pictures in the two-dimensional continuous plane, for instance under certain geometric constraints (the curve is for instance not allowed to cross itself). This question is closely related to phase transitions for models of two-dimensional physical systems (as the phase separation lines are often such random fractal curves when the system is at its critical temperature, where different phases coexist). We shall see that analysis with complex numbers play an important role in the mathematical understanding (and in certain cases in the solution) of this problem.

9 de maio
Instituto Nacional de Matemática Pura e Aplicada às 17:00
Título: Surface fluctuations and their geometries

Abstract: We will first introduce in a heuristic way the natural generalization of Brownian motion to random surfaces i.e. heuristically speaking the random mountains defined in the continuum. We will discuss some basic features of this object called the Gaussian Free Field, such as its lack of continuity and we will discuss recent work that enable to describe its topography, focusing on the analogy with one-dimensional Brownian motion. This will be based on work by and joint work with Scott Sheffield, Jason Miller and Hao Wu.