ENG 
ESP Plenary talks
These lectures will be accessible live only to registered participants via Zoom. You can find the Zoom link to join on our forum.
Monday, July 19, 12:15 ~ 13:15 UTC-3
On the coniveau of algebraic varieties
Claire Voisin
CNRS, IMJ-PRG, France - This email address is being protected from spambots. You need JavaScript enabled to view it.
To study the topology of a complex algebraic variety, it is natural to try to understand which homology classes are supported on closed algebraic subvarieties of a given dimension. We will describe classical and recent results on this question, and relate these develoments to the rationality problem, which asks for necessary criteria for a variety to be birational to affine space.
Monday, July 19, 14:45 ~ 15:45 UTC-3
Algebraic intersections in analysis
Miguel Walsh
Universidad de Buenos Aires, Argentina - This email address is being protected from spambots. You need JavaScript enabled to view it.
We will discuss some results about the asymptotic behavior of families of polynomials and algebraic varieties that play a role in several parts of analysis and the extent to which their applications may reflect different manifestations of a single phenomenon.
Tuesday, July 20, 13:30 ~ 14:30 UTC-3
Volumes of hyperbolic 3-manifolds
Ian Agol
University of California at Berkeley, United States of America - This email address is being protected from spambots. You need JavaScript enabled to view it.
Jorgensen and Thurston showed that the volumes of hyperbolic 3-manifolds form a well-ordered set. After an introduction to these topics, we will give a survey of what is known about the smallest volume hyperbolic manifolds in various classes and corresponding to various ordinals.
Wednesday, July 21, 13:30 ~ 14:30 UTC-3
Towards Better Algorithms for Graph Crossing Number
Julia Chuzhoy
Toyota Technological Institute at Chicago, United States - This email address is being protected from spambots. You need JavaScript enabled to view it.
Graph Crossing Number is a fundamental and extensively studied problem with wide ranging applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. The problem is known to be notoriously difficult, and despite extensive work, it is still poorly understood from many different angles. In this talk we will focus on the algorithmic aspect of the problem. As the problem is known to be NP-hard, it is natural to look for efficient algorithms that solve the problem approximately. We will survey some known techniques for designing efficient (approximate) algorithms, and discuss some new promising directions in this area.
Joint work with Sepideh Mahabadi (Toyota Technological Institute at Chicago) and Zihan Tan (University of Chicago).
Thursday, July 22, 13:30 ~ 14:30 UTC-3
Replica Symmetry Breaking for Sparse Random Constraint Satisfaction Problems
Allan Sly
PrincetonUniversity, United States - This email address is being protected from spambots. You need JavaScript enabled to view it.
Ideas from physics have predicted a number of important properties of random constraint satisfaction problems such as the satisfiability threshold and the free energy (the exponential growth rate of the number of solutions). Another prediction is the condensation regime where most of the solutions are contained in a small number of clusters and the overlap of two random solutions is concentrated on two points. We establish this phenomena for the first time in sparse CSPs in the random regular NAESAT model.
Joint work with Danny Nam (Princeton University) and Youngtak Sohn (Stanford University).
Friday, July 23, 13:30 ~ 14:30 UTC-3
Wave maps into the sphere
Carlos Kenig
University of Chicago, United States of America - This email address is being protected from spambots. You need JavaScript enabled to view it.
We will introduce wave maps, an important geometric flow, and discuss, for the case when the target is the sphere, the asymptotic behavior near the ground state (without symmetry) and recent results in the general case (under co-rotational symmetry) in joint work with Duyckaerts, Martel and Merle.