1998 seminars

Pedro Lopes, Instituto Superior Técnico
To be announced

Primeira palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

Paulo Semião, Universidade do Algarve
To be announced

Segunda palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

Marko Stosic, ISR
To be announced

Terceira palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

Marco Mackaay, Universidade do Algarve
To be announced

Quarta palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

João Martins, Instituto Superior Técnico
To be announced

Quinta palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

Rui Carpentier, Instituto Superior Técnico
To be announced

Sexta palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

Roger Picken, Instituto Superior Técnico
To be announced

Sétima palestra dum Mini-Encontro do projecto "Topologia Quântica", onde haverá apresentações curtas e informais de membros do projecto sobre assuntos de interesse actual. Todos os interessados bem-vindos.

Pierre Cartier, Institut des Hautes Études Scientifiques
New methods in renormalization theories - I

The first occurence of the ideas of renormalisation in physics is due to Green, around 1850, who used such methods to study the motion of a pendulum in a fluid. The same kind of methods was proposed by J. Oppenheimer around 1930, to take in account the so-called radiative corrections to the spectral lines of atoms. Like the previous attempts in classical electrodynamics, this approach led to unphysical infinite quantities. As it si well-known, the new methods of Bethe, Schwinger, Tomonaga, Feynman and Dyson solved in principle the problem of infinities around 1950. But a conceptual breakthrough occured ten years ago when A. Connes and D. Kreimer introduced Hopf algebraic methods in this game. We propose to explain our own verion of these methods, emphasizing a certain infinite-dimensional group, the so-called dressing group. A striking feature is the deep analogy with groups introduced by Grothendieck under the name of motivic Galois groups. These lectures shall begin with a short historical review, followed by a description of the standard calculations, and then we shall describe in detail the new methods.

Yassir Dinar, International School for Advanced Studies (SISSA), Trieste
Algebraic Frobenius manidolds and primitive conjugacy classes in Weyl group

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to the loop algebra proved to be equivalent to a generalized Drinfeld-Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.

Ugo Bruzzo, International School for Advanced Studies (SISSA), Trieste
Instantons and framed bundles on rational surfaces

The talk concerns a correspondence between framed instantons on the one-point compactification of an affine complex surface X, and framed holomorphic bundles on a projective completion of X. This correspondence is known for X the affine plane (Donaldson) and X the affine plane blown up at a point (King). After reviewing these cases, I will discuss possible generalizations (basically, when the projective completion is a rational surface). I will also spend some words on instanton countings on these surfaces. Physically this corresponds to studying the Nekrasov partition function for topological super Yang-Mills theories on X.