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João Nuno Tavares, Faculdade de Ciências, Universidade do Porto

Introduction to deformation quantization

Topological Quantum Field Theory Seminar

João Nuno Tavares, Faculdade de Ciências, Universidade do Porto

Introduction to deformation quantization

Preparatory material for deformation quantization distributed during the meetings by Joao Nuno.

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

José Mourão, Instituto Superior Técnico

Introduction to F-theory II

Continuation of the study of aspects of the relation between

- moduli spaces of flat ${E}_{8}$ connections on elliptic curves,
- the deformation of complex structures on Del Pezzo surfaces and,
- 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 .

Joao Nuno Tavares, Faculdade de Ciências, Universidade do Porto

Introduction to deformation quantization - III

Preparatory material for deformation quantization distributed during the meetings by Joao Nuno.

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.

Reference:

- 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

José Mourão, Instituto Superior Técnico

Vacuum of $N=2$ supersymmetric Yang-Mills theory

Introduction to the solution by Seiberg and Witten of the $N=2$ supersymmetric Yang-Mills theory (following the reference).

- W. Lerche, "Introduction to Seiberg-Witten Theory and its Stringy Origin", hep-th/9611190 .