Matemática

An introduction to impredicative ordinal notation systems

David Fernandéz-Duque
Université Paul Sabatier, Toulouse

Abstract: In this course we will give an introduction to ordinal notation systems based on collapsing cardinals in the style of Buchholz. Although familiarity with proof-theoretic ordinals is assumed, the course will work gradually, beginning with a quick review of predicative notation systems and introducing some intermediate systems along the way. The course will be divided in two sessions.

Formas & Fórmulas

A exposição Formas & Fórmulas mostra como imagens e conceitos da Geometria e da Álgebra interatuam e se completam, ligando fórmulas matemáticas com modelos geométricos, com objetos de uso comum e com formas de arquitetura.

O evidenciar de linhas e superfícies matemáticas e as suas múltiplas visualizações permite criar novos elementos e novas formas, potenciando outras relações e outras visões, concretamente com a Arte.

Predicative ordinal notations (II)

João Enes
CMAFCIO, Universidade de Lisboa

Abstract: In this talk we will present the standard ordinal notation system for ordinals less than $\varepsilon_0$. We will introduce the Veblen hierarchy of functions based on the class of additively indecomposable ordinals. This will allow us to go beyond $\varepsilon_0$ and present a notation system for ordinals less than the Feferman-Schütte ordinal $\Gamma_0$.

Quasi-invariant gaussian measures for the nonlinear wave equation

Nikolay Tzvetkov
Univ. de Cergy-Pontoise

Abstract: We will show that a natural class of gaussian measures living on Sobolev spaces of varying regularity are quasi-invariant under the flow of the two dimensional cubic defocusing wave equation. For that purpose, we introduce renormalised energies and we establish the associated energy estimates.
This is a joint work with Tadahiro Oh (Edinburgh University).

Predicative ordinal notations (I)

João Enes
CMAF-CIO, Universidade de Lisboa

Abstract: In this talk we will present the standard ordinal notation system for ordinals less than $\varepsilon_0$. We will introduce the Veblen hierarchy of functions based on the class of additively indecomposable ordinals. This will allow us to go beyond $\varepsilon_0$ and present a notation system for ordinals less than the Feferman-Schütte ordinal $\Gamma_0$.

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