Current Geometry

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

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'

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

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

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

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