Recentes progressos e desafios na geração de música por aprendizagem profunda/
Seminário de Matemática Aplicada e Computacional:
William Shadwick.
- Rio de Janeiro: IMPA, 2020.
- video online
Resumo: More than a century ago, Elie Cartan produced a collection of powerful methods for addressing problems that were, and remain, central to mathematics. The initial impact of this work was the solution of a major outstanding problem of the time, the classification of infinite dimensional Lie pseudogroups. But Cartan’s tools have applications well beyond the study of pseudogroups, namely the systematic discovery of the truly intrinsic features—differential invariants and symmetry groups that are independent of any choice of local coordinates from a given group of coordinate transformations. I will give an overview of Cartan’s machinery and survey a variety of applications and potential applications in geometry, dynamical systems, probability and numerical analysis. .