TQFT Club Meeting 30-Mar-2000

12.30 Lunch party meets at Restaurante "Rota do Colombo" (previously called "O Mimo"). All welcome.

Afternoon Session

Room 3.10 Mathematics Department, IST

14.00 - 15.15 João Nuno Tavares (Faculdade de Ciências, Universidade do Porto)

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 referencias 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.

15.30 - 16.45 Gustavo Granja (Instituto Superior Técnico)

Summary: 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).

16.45 Tea & chocolate biscuits!

DATE: Thursday, 30/03/2000

VENUE: Mathematics Department, Room 3.10

URL: http://www.math.ist.utl.pt/~rpicken/tqft