Anteriores Colóquios de Matemática do Complexo Interdisciplinar

New integrable dynamical systems of relativistic invariance

J. P. Françoise
(Univ. Paris VI, França)

30 de Outubro de 1997 (quinta-feira), 16:00 · Complexo Interdisciplinar, Anfiteatro

S. Ruijsenaars and his school introduced integrable dynamical systems of relativistic invariance (classical and quantic). A Lax pair approach was latter proposed by M. Bruschi and F. Calogero (CMP, 85). In this talk, I will report on a recent joint work with F. Calogero in which we introduce a new presentation of these systems based on the associated second-order differential equation. We solve a conjecture posed last year by F. Calogero (to appear in JMP) on the solution of certain perturbations of these systems with completely periodic trajectories.

A hundred years of group representation

J. A. Green
(University of Warwick, Conventry, Grã-Bretanha)

30 de Abril de 1997 (quarta-feira), 16:00 · Complexo Interdisciplinar, Anfiteatro

In 1897 G. Frobenius described for the first time the now familiar notion of the matrix representations of a group, and explained their relation to group characters. The new theory gave remarkable and deep results in finite group theory. But it soon became clear that the representations of classical groups were involved in many problems of harmonic analysis, geometry and quantum physics. Group representations continue to be involved in many, strikingly varied, advances in mathematics and theoretical physics in the present day.

Ergodicité asymptotique en Analyse Stochastique

Paul Malliavin
(Univ. Paris VI / Acad. Sciences, França)

23 de Abril de 1997 (quarta-feira), 16:00 · Complexo Interdisciplinar, Anfiteatro

Certains systèmes stochastiques après une evolution pendant un temps long tendent a se "stabiliser" en décrivant un processus stationnaire du type de Ornstein-Uhlenbeck. On discutera deux tels systemes, l'un provenant de mathématique appliquée, l'equation du filtrage de Zakai, l'autre de la théorie des groupes en dimension infinie, la recherche de représentations ergodiques fidèles. Dans ce type de problèmes il est indispensable de disposer d'estimations a priori qui seules permettent de confiner le système en montrant que son explosion ne peut pas se produire. Dans le premier cas l'estimation a priori proviendra du Calcul des variations stochastiques; dans le second cas de la positivité d'un tenseur de Ricci en dimension infinie.

The Axiom of Countable Choice and point-free topology

Bernhard Banaschewski
(McMaster University, Hamilton, Ontario, Canadá)

16 de Abril de 1997 (quarta-feira), 16:00 · Complexo Interdisciplinar, Anfiteatro

A discussion of various aspects of the curious fact that the ACC is very close to the condition that coproducts of Lindelöf frames are Lindelöf while its counterpart for compactness is true without any choice principle---which contrasts with the classical result that the Tychonoff Product Theorem is equivalent to the Axiom of Choice.

Singularidades de Superfícies e Combinatória

Le Dung Trang
(CNRS, França)

9 de Abril de 1997 (quarta-feira), 16:00 · Complexo Interdisciplinar, Anfiteatro

Seja C uma curva de uma superfície complexa lisa X. Sejam C(i) as componentes irredutíveis de C. É possível definir uma matriz simétrica M(C) associada a C, a matriz de intersecção de C. Se essa matriz for definida negativa, um teorema de Grauert demonstra que a contracção de C define uma superfície singular. Quando as componentes de C são isomorfas a uma curva racional não singular e se cortam transversalmente, podemos associar um grafo à curva. Invariantes do grafo definem invariantes da geometria da singularidade da superfície associada. Obtemos assim uma classe de grafos com um significado geométrico. Recentes investigações usando estas técnicas permitiram obter novos resultados sobre singularidades de superfícies.

Théorème de Baire, séries de Fourier et séries de Taylor

Jean-Pierre Kahane
(Univ. Paris XI, Orsay, França)

13 de Fevereiro de 1997 (quinta-feira), 15:00 · Complexo Interdisciplinar, Anfiteatro

Classification of projective curves

Ciro Ciliberto
(Univ. de Roma II, Itália)

8 de Janeiro de 1997 (quarta-feira), 16:00 · Complexo Interdisciplinar, Anfiteatro

In this talk I will give an account of classical results by Halphen Noether, Castelnuovo, etc., on relations between the invariants of curves in projective spaces. Then I will present recent developments of the subject and focus on some open problems concerning the classification of families of curves in projective spaces.

Pode também consultar os anúncios de colóquios a realizar.

URL: http://alf3.cii.fc.ul.pt/gfm/Events/math_colloquia_past.pt_PT.html
Last modified: 1997 Oct 20 16:36:43 WEST