1998 seminars

Carlos Florentino, Instituto Superior Tecnico
Geometric methods in integrable systems

Study equations in Lax form and understand how they give rise to a spectral curve and a line bundle on it.


  • Mumford, D. "Tata Lectures on Theta, vol II", Progress in Math. 43, Birkhauser 1984
  • Beauville, A. "Jacobiennes des courbes spectrales et systemes hamiltoniens completement integrables", Acta Math. 164, '90

José Mourão, Instituto Superior Técnico
Introduction to F-theory II

Continuation of the study of aspects of the relation between

  1. moduli spaces of flat E 8 connections on elliptic curves,
  2. the deformation of complex structures on Del Pezzo surfaces and,
  3. singularities on these surfaces,

are studied. The motivation comes from work on "F-theory" by Friedman, Morgan and Witten.


  • R. Friedman, J. Morgan and E. Witten, "Vector Bundles and F theory" hep-th/9701162
  • R. Friedman, J. Morgan and E. Witten, "Vector Bundles over Elliptic Fibrations", alg-geom/9709029.
  • R. Friedman, J. Morgan and E. Witten, "Principal G-bundles over elliptic curves", alg-geom/9707004 .

Margarida Mendes Lopes, Faculdade de Ciencias, Universidade de Lisboa
Blow-up of points in almost general position and Del Pezzo surfaces

Geometric description of singularities in Del Pezzo surfaces.


  • J.-Y. Merindol, "Les Singularites Simples Elliptiques, Leurs Deformations, les Surfaces Del Pezzo et les Transformations Quadratiques", Ann. Scient. Ec. Norm. Sup., 4 serie, 15 (1982) 17-44