### Minicursos

**Plenarista:**Ana Paulina Figueroa Gutierrez, ITAM

**Titulo:**Graph Theory: Bridging mathematics

**Resumo:**Compared to classic areas of mathematics such as algebra, analysis, or geometry, graph theory has a very recent development, with most of its results having been published in the last 60 years. Graph theory studies objects called graphs, which are constructed from a set and the relationships between its elements. The simplicity of the definition of a graph allows a number of problems from multiple origins to be formulated in its terms, and this may be the secret of its success. For example, the theory of computation, another young area with a significant impact, has an almost romantic relationship with graphs and combinatorics. In these sessions, we will study some applications of classical concepts in graph theory and notice how it easily connects with other areas of mathematics such as geometry, topology, and algebra. This course is designed for any recently graduated student, regardless of whether they have taken courses in graph theory or not.

**Plenarista:**Eduardo Teixeira, University of Central Florida

**Titulo:**Mini-course: an introduction to free boundary problems

**Resumo:**I will describe the mathematical theory of the obstacle problem.

**Plenarista:**Emanuel Carneiro, ICTP - Trieste

**Titulo:**Fourier optimization and number theory

**Resumo:**Some problems in number theory are naturally related to different types of oscillatory structures. In such situations, certain Fourier optimization problems emerge, carrying important information about the original number theoretical entity and also being of intrinsic interest in analysis.

The aim of this minicourse is to present a variety of number theory problems which are amenable to a Fourier optimization framework. These include: (i) bounding objects related to the Riemann zeta-function; (ii) estimating the size of prime gaps; (iii) bounding the pair correlation of zeros of the Riemann zeta-function; (iv) bounding the height of low-lying zeros over families of L-functions; (v) estimating the angular discrepancy of zeros of polynomials; (vi) bounding the least quadratic non-residue modulo a prime; (vii) bounding the least prime in an arithmetic progression.

No previous research background in number theory is required (at least to have an idea of what the minicourse is about); we will briefly review the main tools and definitions as we move along.

**Plenarista:**Zdzislaw Brzezniak, University of York

**Titulo:**Stochastic PDEs with constraints

**Resumo:**I will speak about stochastic SPDEs, e.g. Landau-Lisfhitz-Gilbert, Navier-Stokes or wave Equations, whose solutions satisfy certain constraints, e.g. the values take values in a manifold, or the $L^2$ norm is equal to $1$.