Plenarista: Claudia Alejandra Sagastizabal (Universidade de Campinas)
Titulo: Industrial mathematics in action
Resumo: An industrial m+A1:C14athematician combines analytical and problem-solving skills, built upon a background of mathematical theory, computing, statistics. To illustrate these features, we present an industrial application involving advanced tools of mathematical optimization. Specifically, we shall discuss the theory of optimal mass transportation, and its use in geosciences for full-waveform inversion, a seismic imaging technique.


  Plenarista: Daniel Remenik (Universidad de Chile)
Titulo: Integrable fluctuations in one-dimensional random growth
Resumo: The KPZ universality class is a broad collection of one-dimensional random growth models which share a common, very rich fluctuation behavior. This common behavior is characterized by a special scaling invariant Markov process, known as the KPZ fixed point, which arises as the universal scaling limit of all models in the class. In this talk I'm going to introduce this object and present explicit formulas for its transition probabilities, which are obtained from certain special models in the class. I will then explain how these formulas lead to connections between the fluctuations of KPZ models and some classical completely integrable systems, the Kadomtsev-Petviashvili PDE for the KPZ fixed point and the Toda lattice for a special microscopic model in the class.
  Plenarista: José Seade (Universidad Nacional Autónoma de México)
Titulo: Chern classes and indices of vector fields on singular varieties
Resumo: Chern classes of manifolds and vector bundles are fundamental invariants in geometry and topology, and these are much related to indices of vector fields (or sections of bundles). The analogous theory for singular varieties has been developed since the 1960s by various authors, and even so we can say that it is still in its childhood. In this talk we shall revise some aspects of this theory. I will speak mostly on joint work with Roberto Callejas-Bedregal and Michelle Morgado.
  Plenarista: Simon Griffiths (Pontifícia Universidade Católica do Rio de Janeiro)
Titulo: Recent results in Ramsey Theory
Resumo: Ramsey Theory is the study of inevitable structure, with examples occurring in various areas, including Graph Theory, Number Theory and Geometry. We discuss recent results on Ramsey numbers, including the exponential improvement for diagonal Ramsey numbers.
  Plenarista: Sonia Natale
Titulo: Extensions of Hopf algebras and tensor categories
Resumo: In this talk we shall discuss the notion of extension of Hopf algebras and its relation to the more general notion of extension of tensor categories.
We shall discuss the problem of deciding if certain classes of Hopf algebras and tensor categories are closed under extensions. Then we shall present a family of Hopf algebras obtained by a process of cofinite central extension from a Noetherian Hopf algebra and a subgroup of the algebraic group of characters of a central Hopf subalgebra and discuss several of its main features.