Data: 14/09/2016 (quarta feira)
Hora: 13:30 h
Palestrante: Emanuel Carneiro (IMPA)
Título: Regularity of fractional maximal operators
Resumo: In this talk we discuss the recent developments on the regularity
theory of maximal operators, when these act on Sobolev and BV functions. Among
other things, we shall discuss boundedness and continuity results for the
one-dimensional fractional Hardy-Littlewood maximal operator in the continuous
and discrete settings.
This is based on a joint work with Jose Madrid (Aalto University - Finland).
Data: 13/07/2016 (quarta feira)
Hora: 13:30 h
Palestrante: Udayan Darji
Título: Some Examples of Universality in Dynamics
Resumo: In this talk we discuss two types of dynamical systems. Once concerns the dynamics of linear maps on separable Banach spaces and the other concerns dynamical systems on the Cantor set. It is well-known that dynamics of compact metric spaces can be captured by the dynamics of the Cantor space. More precisely, if (X,f) is a dynamical system with X a compact metric space and f is continuous, then (X,f) is a factor of some (C,g) where C is the antor space and g is continuous self-map of C. Hence, in some sense Cantor set is universal for dynamics of compact metric spaces. The type of questions we discuss concerns given a large class of dynamical systems, can we find one “super” or “universal” dynamical system such that every system in the given class is a factor of this “universal” dynamical system? This is joint work with Etienne Matheron. The results of this talk will appear in Proceedings of the AMS.
Palestrante: Reimundo Heluani (IMPA)
Título: Special holonomy and representation theory of vertex algebras
Resumo: To any smooth manifold M one can attach a vertex operator superalgebra V in a canonical way. When M has special holonomy the character of V is expected to have special modular properties, for example, if M is Calabi-Yau, the character of V is a weak Jacobi form. Also in the case when M has special holonomy, V admits commuting embeddings of certain special W algebras. The characters of representations of W turn out not to be modular but rather mock modular forms. When one decomposes the character of V in terms of characters of W, the generating sequence, besides being Mock modular itself for trivial reasons, shows some striking connections with the theory of finite simple groups. We will describe the situation in the case when M is a K3 surface, which after an observation of Eguchi, Ooguri and Tachikawa is expected to have connections with Mathieu's M24 group as well as give some speculations as to what may happen in the other special holonomy cases.