# TQFT Club Meeting 8-Apr-1999

# Note:

### Exceptionally, we are organizing the April Meeting of the TQFT club at Complexo Interdisciplinar of the University of
Lisbon (Av. Prof Gama Pinto 2, 1649-003 LISBOA), where the afternoon's proceedings will take place (so that participants can attend the
colloquium by Fields medallist Efim Zelmanov on *"What makes a group finite?"*)

####
12.15 Lunch at the Cafeteria of Complexo Interdisciplinar of the Univ. of
Lisbon

##

Afternoon Session

####
Room B1-01 of Complexo Interdisciplinar of the University of
Lisbon

###
13.40 - 14.40
(Algebraic geometry and integrable systems - 4th session) José Mourão (Instituto Superior Técnico)

### "Moduli space of curves, abelian integrals and integrable systems"

Summary: We describe Krichever and Phong's space of "geometric data"
wchich consists of specific bundles over the moduli space of curves.
These bundles are foliated in a natural way by symplectic
manifolds which have the structure of completely integrable systems
(with a natural system of action-angle variables). It turns out that
many of the known integrable systems fall into this category.
We also describe the role of the Whitham hierarchy in this context.

References:

- I.M. Krichever and D.H. Phong, "On the integrable geometry of soliton equations and N=2 supersymmetric gauge", J.Diff.Geom. 45 (1997) 349--389, hep-th/9604199
- I.M. Krichever and D.H. Phong, "Symplectic forms in the theory of solitons", hep-th/9708170
- I.M. Krichever, "The tau-function of the universal Whitham hierarchy,
matrix models and topological field theories", Comm. Pure Appl. Math. 47 (1994) 437--475." hep-th/9205110

###
14.50 - 15.50 (Seminar) Michael Paluch (Instituto Superior Técnico)

###
"Elliptic Spectra and the Witten Genus"

Summary: Genus is a rule which assigns to a closed oriented manifold M a
complex number G(M); in addtion G sends disjoint unions to sums, products
to products, and is a cobordism invariant. Thus G is a ring homomorphism
from Thomīs oriented cobordism ring to the complex numbers. One example
of a genus is the Witten genus, and it can be realized as a map of ring
spectra.

References:

- Mike Hopkins and Mark Mahowald, "From elliptic curves to homotopy theory", dvi file
- M. J. Hopkins, M. Ando, and N. P. Strickland, "Elliptic spectra, the Witten genus, and the theorem of the cube", dvi file

###
16.00 - 17.00 We plan to attend the colloquium by Fields medallist Efim Zelmanov on *"What makes a group finite?"* organized by the Mathematics
Department of Lisbon University at the Anfiteatro of Complexo Interdisciplinar.

####
17.00 - 17.30 Tea at the Bar of Complexo Interdisciplinar of the Univ. of
Lisbon

DATE: Thursday, 8/04/99

VENUE: Room B1-01 of Complexo Interdisciplinar of the University of
Lisbon

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

picken@math.ist.utl.pt