Brice Mbombo: Ramsey properties for finite dimensional normed spaces

Data: segunda-feira, 25 de maio de 2015, às 13h30

Sala: 249-A

Palestrante: Brice Mbombo, IME-USP

Título: Ramsey properties for finite dimensional normed spaces

Resumo: Given $d\leq m$, let $\mathbb{E}_{d,m}$ be the set of all $m\times d$ matrices $(a_{i,j})$ such that:

  • $\sum_{j=1}^d |a_{i,j}|\le 1$ for every $1\leq i\leq m$.
  • $\max_{i=1}^m |a_{i,j}|=1$ for every $1\leq j\leq d$.
These matrices  correspond to the linear isometric embeddings from the normed space $\ell_\infty^d$into $\ell_\infty^m$, in their unit bases.

Using the Graham-Rothschild Theorem on partitions of finite sets, we prove the following: for every integers $d$, $m$ and $r$ and every $\varepsilon>0$ there exists $n\geqslant m$ such that for every coloring of $\mathbb{E}_{d,n}$ into $r$-many colors there is $A\in\mathbb{E}_{m,n}$ and a color $\widetilde{r}<r$ such that $A\cdot \mathbb{E}_{d,m} \subseteq$ $(c^{-1} \{\widetilde{r}\})_{\varepsilon}$. As a consequence, we obtain that the group of linear isometries of the Gurarij space is extremely amenable. 

This is a joint work with Dana Bartosová (University of São Paulo) and Jordi Lopez-Abad (ICMAT Madrid).

Dana Bartosova: Where topological dynamics, Ramsey theory and model theory meet

Data: segunda-feira, 18 de maio de 2015, às 13h30

Sala: 249-A

Palestrante: Dana Bartosova, IME-USP

Título: Where topological dynamics, Ramsey theory and model theory meet

Resumo: We recall the connection between the dynamics of automorphism groups of homogeneous structures and the structural Ramsey theory. We will talk about the recent developments and open questions in the area. This is partially a joint work with Aleksandra Kwiatkowska (UCLA).

Yolanda Moreno: Open problems in the theory of separably injective spaces

Data: segunda-feira, 11 de maio de 2015, às 13h30

Sala: 249-A

Palestrante: Yolanda Moreno, Universidad de Extremadura

Título:  Open problems in the theory of separably injective spaces

Resumo: To be announced