Wilson Cuellar Carrera: Estruturas complexas compatíveis no espaço de Kalton-Peck

Data: sexta-feira, 23 de maio de 2014, às 14h

Sala: 243-A

Palestrante: Wilson Cuellar Carrera, IME-USP

Título: Estruturas complexas compatíveis no espaço de Kalton-Peck

Resumo: Dado um espaço de Banach real $X$, uma estrutura complexa em $X$ é um operador linear limitado $J$ em $X$ tal que $J^2=-Id$. Isto induz em $X$ uma estrutura de $\mathbb{C}$-espaço vetorial mediante a multiplicação por escalares: $(a+ib)x= ax + bJx$, para todos $a,b$ reais e $x$ em $X$.

O espaço $Z_2$ de Kalton-Peck é uma soma torcida não trivial de $\ell_2$ com $\ell_2$. Um problema ainda aberto é determinar se $Z_2$ é isomorfo a seus hiperplanos. Nessa direção estudamos estruturas complexas em $Z_2$, estruturas complexas de $\ell_2$ que sejam compatíveis com $Z_2$ ou com seus hiperplanos. Trabalho conjunto com os professores J. M. Castillo, V. Ferenczi, Y. Moreno.

Dana Bartosova: Lelek fan via the projective Fraïssé theory

Data: sexta-feira, 16 de maio de 2014, às 14h

Sala: 243-A

Palestrante: Dana Bartosova, IME-USP

Título: Lelek fan via the projective Fraïssé theory

Resumo: This is going to be part 1 of the series whose part 2 was presented last week. We describe a well-known continuum called the Lelek fan as a natural quotient of a projective Fraïssé limit of finite ordered trees.This model-theoretic approach allowed us to get new results about the Lelek fan and its group of homeomorphisms (e.g. the group of homeomorphisms has a dense conjugacy class). Some results are however purely topological, for instance simplicity of the group of homeomorphisms. At the end, we make the connection between the dynamics of the group of homeomoprhisms and the Gowers' Theorem, which will be the content of part 3. This is a joint work with Aleksandra Kwiatkowska.

Dana Bartosova: Generalization of Gowers' $c_0$ Theorem and its applications in topological dynamics

Data: sexta-feira, 09 de maio de 2014, às 14h

Sala: 243-A

Palestrante: Dana Bartosova, IME-USP

Título: Generalization of Gowers' $c_0$ Theorem and its applications in topological dynamics

Resumo: Gowers proved his famous result on stability of real valued Lipschitz functions on the unit sphere of $c_0$ in 1992. The core of the proof lies in a combinatorial result  of Ramsey type. Since then, many new proofs have appeared. We generalize the theorem and its variations. The original motivation comes from our study of the universal minimal flow of the group of homeomorphisms of a continuum known as a Lelek fan. We will explain the original Gowers' result and our generalizations, give main ideas of the proofs and show how this connects to the original problem. This is a joint work with Aleksandra Kwiatkowska.