Speakers list

**Francesco Baldassarri:**

*Title:* Algebraic Poincare' duality and Dwork's Dual
Theory

*Abstract*: Most of this material is contained in a joint book with
Y. Andre' : *De Rham Cohomology of Differential Modules on Algebraic
Varieties*, to appear soon in the series "Progress in Mathematics" by
Birkhauser.
We use Deligne's definition of "direct image with compact supports" in the
algebraic setting of coherent cohomology, to define De Rham cohomology with
(algebraically) compact supports of a smooth (open) variety over a field of
characteristic zero. We obtain an algebraic version of Poincare' duality.
We show that it coincides with Dwork's "algebraic dual theory".

**Serguei Barannikov:**

*Title:*Quantum periods

**Ugo Bruzzo:**

*Title:*Mirror symmetry for families of Lagrangian tori

**Alberto Collino**

*Title:* Indecomposable higher Chow Cycles on Jacobians

*Abstract:* This is a report on joint work with N. Fakhruddin. We
construct some natural cycles with trivial regulator in the higher Chow
groups of Jacobians. For hyperelliptic curves we use a criterion due to J.
Lewis to prove that the cycles we construct are indecomposable, and then
use a specialization argument to prove indecomposability for more general
curves.

*Address:*Dipartimento di Matematica, Universita' di Torino, Via
Carlo Alberto 10 - 10123 Torino - Italy

*Email:*collino@dm.unito.it

**Ciro Ciliberto:**

*Title:* On the classification of surfaces of general type with non
birational bicanonical map

*Abstract:* In this short talk I will briefly update the state of the art
on the classification of surfaces of general type with non birational
bicanonical map. In particular I will describe the new results on the
subject concerning irregular surfaces with *p_g=q=2* (in
collaboration with M. Mendes Lopes).

*Address:*Dipartimento di Matematica, Universita' di Roma
'Tor Vergata'

*Email:*
cilibert@mat.uniroma2.it

**Dmitri Fuchs:**

*Title:* Chekanov-Eliashberg invariants of Legendrian knots in the
standard contact space.

*Abstract:* A Legendrian curve is a smooth curve in space with zero
restriction of the standard contact form ydx-dz. Within a topological
isotopy type of knots, Legendrian isotopy type are distinguished by two
integer-valued invariants: Thurston-Bennequin Number (TB) and Maslov number
(M). In 1997, Yu. Chekanov and Ya. Eliashberg independently constructed
a new invariant (CE) which can distinguish topologically isotopic
Legendrian knots with equal TB and M. However, the construction of CE is
complicated, and, so far, only one example of Legendrian knots
distinguishable only by CE has been known. I will show that for Legendrian
knots whose diagrams satisfy a certain easy-to-check condition, the
simplest CE invariant can be applied more or less without computations.
This gives rise to a big amount of new examples of knots distinguishable by
CE only.

*Address:*University of California - Davis

*Email:*
fuchs@math.ucdavis.edu

**Lambertus van Geemen:**

*Title:* Half twists of Hodge structures and ball
quotients.

**Hubert Goldschmidt:**

*Title:* Infinitesimal spectral rigidity of symmetric spaces.

**Johan van de Leur:**

*Title:*Twisted Loop Groups, Grassmannians and Frobenius Manifolds

*Abstract:* In the early 90's B. Dubrovin noticed that the local
classification of massive topological field theories can be solved by
classifying certain flat diagonal metrics. Vanishing of the curvature of
these metrics can be written in the
form of a system of partial differential equations,
which is known under the name the Darboux-Egoroff system.
>From solutions of this system one can locally construct Frobenius manifolds.

In this talk I will show that the all tau-functions of the (n-component) KP
hierarchy, which are related to the
twisted loop group of $GL_n$, give solutions of this Darboux-Egoroff system.
Using the Geometry of the Grassmannian we construct from the
corresponding wave function the Frobenius manifold, the deformed
flat coordinates of the metric and the corresponding solution of
the Witten--Dijkgraaf--E. Verlinde--H. Verlinde equations.

*Address:*Department of Mathematics, P.O. Box 80010, 3508 TA Utrecht,
The Neterlands

*Email:*
vdleur@math.uu.nl

**Le Dung Trang:**

*Title:* Combinatorial Trends in Geometry

**Marco Manetti:**

*Title:* Extended deformation functors

**Luca Migliorini:**

*Title:* The hard Lefschetz property and the topology of
semismall maps

**Kieran O'Grady:**

*Title:* New compact hyperkähler manifolds

**Giuseppe Pareschi:**

*Title:* Global generation of coherent sheaves on abelian varieties and applications

**Ziv Ran:**

*Title:* Boundedness of Fano varieties

**Yuli Rudyak:**

*Title:* On strict category weight and the Arnold conjecture

**Gianni Sparano:**

*Title:* On Ricci-flat 4-dimensional manifolds

**Alexandre M. Verbovetsky:**

*Title:* Horizontal cohomology of
differential equations

**Alexandre M. Vinogradov:**

*Title:* A Presentation of Secondary Calculus

Questions and suggestions should go to curgeo@tiros.dmi.unisa.it