Tóm tắt báo cáo

1. Claudio Arezzo
Title: Metrics of constant curvature on Algebraic Manifolds
Metrics of constant curvature have always been thought as the best riemannian metrics we can equip a given manifold with. In the first part of the talk I will explain few classical reasons supporting this belief and  some of the subtleties we face proving their existence.
In particular real and complex manifolds behave very differently depending on which curvature (Sectional, Ricci, scalar…) one tries to make constant.
In the second part of the talk I will focus on the complex case, introducing some fundamental obstructions and analysing if and when few basic geometric operations such as Galois coverings, blow ups and resolutions of singularities preserve the existence of such metrics.
A number of open problems will be discussed.
2. Nguyễn Việt Anh
Title: Ergodic theorems for laminations and foliations: recent results and perspectives
This report discusses recent results as well as new perspectives in the ergodic theory for hyperbolic Riemann surface laminations, with an emphasis on singular holomorphic foliations by curves. The central notions of these developments are directed positive harmonic currents, multiplicative cocycles and leafwise Poincar ́e metric. We deal with various ergodic theorems for such laminations: Random Ergodic Theorem, Geometric Birkhoff Ergodic Theorem, Oseledec Multiplicative Ergodic Theorem and Unique Ergodicity Theorems. Applications of these theorems are also given. In particular, we define and study the canonical Lyapunov exponents for a large family of singular holomorphic foliations on compact projective surfaces. 
Topological and algebro-geometric interpretations of these characteristic numbers are also treated. These results highlight the strong similarity as well as the fundamental differences between the ergodic theory of maps and that of Riemann surface laminations.

Keywords: Riemann surface lamination, singular holomorphic foliation, positive har-monic currents, multiplicative cocycles, leafwise Poincar ́e metric, ergodic theorems, Lya-punov exponents.
3. Yves Andre
Title: Singularities and perfectoid geometry
his will be an overview of recent work by the speaker and of some subsequent works, on applications of perfectoid geometry to homological commutative algebra and singularity theory. The progresses take place primarily in mixed characteristic, but also provide a bridge between characteristic p and characteristic 0.  
4. Amie Wilkinson
Title: Mechanisms for Chaos
5. Benson Farb 
Title: Resolvent degree and Hilbert’s 13th Problem