# 1998 seminars

## 22/01/1998, Thursday, 15:20–16:20

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.

References:

• 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

## 22/01/1998, Thursday, 16:50–17:50

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.

#### References

• 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 .