1998 seminars

Gonçalo Rodrigues, Instituto Superior Técnico
To be announced

Carlos Florentino, Instituto Superior Técnico
To be announced

João Nuno Tavares, Faculdade de Ciências, Universidade do Porto
Sobre o método do referencial móvel de E. Cartan

Bibliografia:

A. Na exposição seguirei muito de perto:

  1. Cartan Elie, La theorie des groupes finis et continus et la geometrie differentielle. Gauthiers-Villars, 1937.
  2. Cartan Elie, La methode du repere mobile, la theorie des groupes continus et les espaces generalises. Hermann, 1935.

B. Outras referências mais actuais e avançadas (que eu não vou abordar):

  1. Griffiths P., On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry. Duke Math. Journal 41 (1974), 775-814.
  2. Griffiths P., Harris J., Algebraic geometry and local differential geometry. Ann. Sci. Ecole Norm. Sup. 12 (1979), 355-452.
  3. Akivis M. A., Goldberg V. V., Projective differential geometry of submanifolds. North-Holland, 1993.
  4. Akivis M. A., Goldberg V. V., Conformal differential geometry and its generalizations. John Wiley and Sons, Inc., 1996.

C. Aplicações (que eu não vou abordar):

  1. Razumov A. V., Frenet Frames and Toda Systems, math.DG/9901023
  2. Fels, M., Olver, P. J., Moving coframes I. A practical algorithm. Acta Appl. Math. 51 (1998) 161-213.
  3. Fels, M., Olver, P. J., Moving coframes II. Regularization and theoretical foundations. Acta Appl. Math. 55 (1999) 127-208.

Gustavo Granja, Instituto Superior Técnico
Elliptic cohomology

I will explain how geometric descriptions of genera determine geometric descriptions of the associated cohomology theories and then give some examples. Then I will try to say something about the case of elliptic genera. For these the geometric description is still not rigorous.

References (I have copies of the non-web references, in case any one is interested):

  1. Haven't looked at this paper but it has a cool title: Dijkgraaf, R.; Moore, G.; Verlinde, E.; Verlinde, H., Elliptic genera of symmetric products and second quantized strings. Comm. Math. Phys. 185 (1997), no. 1, 197--209. hep-th/9608096
  2. Witten, Ed., Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (1987), no. 4, 525--536. Postscript from KEK library
  3. Hopkins, Michael J. Characters and elliptic cohomology. Advances in homotopy theory (Cortona, 1988), 87--104, London Math. Soc. Lecture Note Ser., 139, Cambridge Univ. Press, Cambridge-New York, 1989
  4. M. J. Hopkins, M. Ando, and N. P. Strickland, "Elliptic spectra, the Witten genus, and the theorem of the cube", dvi file
  5. Segal, G. "Elliptic cohomology (after Landweber-Stong, Ochanine, Witten, and others)". Séminaire Bourbaki, Vol. 1987/88. Astérisque No. 161-162, (1988), Exp. No. 695, 4, 187--201 (1989).

Rui Loja Fernandes, Instituto Superior Técnico
To be announced

Peter Gothen, Faculdade de Ciências, Universidade do Porto
To be announced

Marco Mackaay, Universidade do Algarve
To be announced

Sergei Anisov and Edith Elkind, Instituto Superior Técnico
To be announced

Helena Albuquerque, Universidade de Coimbra
To be announced

Miguel Abreu, Instituto Superior Técnico
To be announced

Marco MacKaay, Universidade do Algarve
To be announced

Mark Weber, Macquarie University
To be announced

Andrei Tyurin, Steklov Mathematical Institute
To be announced

Carlos Florentino, Instituto Superior Técnico
To be announced

Sílvia Anjos, Instituto Superior Técnico
To be announced

José Mourão , Instituto Superior Técnico
To be announced

José Natário, Instituto Superior Técnico
To be announced