Date: March 25, 2014
Anfiteatro 0.05

Tema 1.  “Lenguajes” algebraicos en los siglos XVI y XVII

Date: June 25, 2013
Departamento de Matemática, Faculdade de Ciências da Universidade do Porto

Higgs bundles appear in several guises including (a) as solutions to gauge-theoretic equations for connections and sections of a bundle (b) as holomorphic realizations of fundamental group representations or, equivalently, local systems and (c) as special cases of principal bundles with extra structure (principal pairs). Each point of view leads to a construction of a moduli space, i.e.

Date: April 16, 2012
16/04: Room M029; 18/04: Room M007; 20/04: Room M031. Coffee is served before each talk (09h00-09h30).

16/04/2012. Introduction to Theory of Prime Ends

18/04/2012. Applications I: Index of iterates of planar homeomorphisms

20/04/2012. Applications II: Rotation number of planar attractors


Date: January 10, 2012
Edifício da Matemática: Sala 0.31 nos dias 10 e 11; Sala 0.29 no dia 13
Date: September 12, 2011
Sala 0.27

12-15 Setembro. Total de 8 horas.

Date: April 1, 2011
Sala 0.31 - 01/04; 08/04; 15/04 - 14h30

There will be 3 lectures:

- The first is devoted to explaining the main concepts and we will take the opportunity to talk about other statistical properties of dynamical systems, such as Central Limit Theorems, Laws of large numbers or Birkhoff's ergodic theorem, Poincaré's recurrence theorem and Kac's theorem.

Date: November 26, 2010
Sala 0.30 - 26/11; 10/12; 17/12 - 14h30

Lecture 1: Representations of surface groups and harmonic maps

Date: October 22, 2010
Room 0.31, Dep. Matemática. Friday 22/10: 17h-17h50m and Saturday 23: 9h30m-10h20m

In this series of two lectures I will review what we know about moduli space of instanton bundles on projective spaces. We will see that the situation drastically change when the dimension of the projective space increase. At the end of the two talks I will state some interesting open problems.

Date: May 10, 2009
11, 18 and 19th May 2009 11'30 am room 1.25

Graded manifolds are "manifolds where some coordinates anticommute".
Among other things, they provide a way to encode well-known
matematical structures in a geometric and concise fashion.
I plan to cover
- graded linear algebra, graded manifolds,
- how they encode $L_{\infty}$ algebras and Lie algebroids

Date: April 15, 2009
Centro de Matemática da Universidade do Porto

15, 16 e 17 de Abril próximo

Em cada um destes dias haverá duas sessões de duas horas

Os slides do curso estão disponíveis na página:

Date: October 15, 2008
The course will be held on Wednesdays at 15h, place will be announced.

The aim of the course is to introduce pseudodifferential calculus for Lie groupoids and study the index theory of elliptic such operators.

Date: September 17, 2008
Sala 1.02

Lecture 1: 17 September (Wed): 14h30-15h30 (Room 1.02 )

Bundle Theory:

Date: November 28, 2007
Department of pure Mathematics, Faculty of Science of the University of Porto

We shall review some results in the theory of Hopf algebras and their tensor categories of representations, putting special emphasis in the classification problem in the semisimple case. We shall discuss the construction of extensions and semisimple Hopf algebras arising from matched pairs of finite groups as well as the more recent construction of group theoretical Hopf algebras.

Date: October 15, 2007
Primeira aula no dia 15/10 na sala 0.04, às 14h30. Aulas seguintes no dia 18/10 na sala 1.26, às 14h30 e no dia 19/10 na sala 0.03, às 14h30

Lecture 1 (October 15: 14.30-16.00, Room 0.04) : Moduli and quotients

Date: June 4, 2007
Sala 0.05 do edifício das Matemáticas

Sessão 1 - Segunda-feira, 4 de Junho, 14.30-16.00
Classical variational principle and Hausdorff dimension in conformal dynamics

Sessão 2 - Terça-feira, 5 de Junho, 14.30-16.00
Relativized variational principle and Hausdorff dimension in nonconformal dynamics

Date: September 4, 2006
Anfiteatro 0:31, Departamento de Matemática Aplicada, FCUP


Date: June 7, 2006
Anfiteatro 0:30, Departamento de Matemática Aplicada FCUP

Mini curso:
Approximate Solutions of Second Kind Integral Equations

Sessão 1 - Quarta-feira, 7 de Junho, 11h, anf. 0:30
Sessão 2 - Quinta-feira, 8 de Junho, 14 h, anf. 0:30

Date: April 6, 2006
Anfiteatro 0.05

A numerical semigroup is a subset of ${\mathbb N}$ closed under addition, containing the zero element, and with finite complement in ${\mathbb N}$. Even though the concept is easy to understand, there are many pro\-blems related to numerical semigroups that remain unsolved.

Date: November 11, 2005
sala 0.04 Edifício dos Departamentos de Matemática, FCUP

Os Expoentes de Lyapunov medem a taxa exponencial de aproximação, ou afastamento de pontos quando sujeitos a um sistema dinâmico. Neste curso iremos considerar sistemas dinâmicos conservativos como:

Date: May 16, 2005
Dias 16 e 17 de Maio (2. e 3.feira) das 9:30 - 11:00. Sala 1.21 - Edifício dos Departamentos de Matemática, Rua do Campo Alegre, 687

In order to find an approximate solution of an eigenvalue problem Tφ=λφ for a bounded operator T on a Banach space, one often considers a sequence (T_{n}) of bounded operators which converge to T in some sense and then one solves T_{n}φ_{n}=λ_{n}φ_{n}. When the convergence of (T_{n}) to T is slow, one needs to accelerate the convergence of (λ_{n}) to λ and of φ_{n} to φ.