As part of the Dusafest conference, on the morning of Friday Oct 13,
there will be a miniworkshop consisting of five 35minute talks by young researchers.
The miniworkshop will also be held in S240, in the basement of the Math Building.
Coffee and other refreshments will be available, and a light breakfast will
be served in the morning.
Schedule

October 13, 2006 09:15 AM  09:50 AM 
Joseph Johns, NYU
Morse Functions and Lefschetz Fibrations
Let f:N > R be a Morse function and let g be a Riemannian metric such that
(f,g) is MorseSmale. I will explain a construction which, under certain restrictions,
produces a Lefschetz fibration π: T*N > C extending f and having the
same critical points. In addition I will explain a relation between the directed Fukaya category
of π and the flow category of (f,g). If time permits, I will describe
an application to the study of exact Lagrangian submanifolds of T*N, using a spectral s
equence of Seidel. 
October 13, 2006 09:55 AM  10:30 AM 
Brett Parker, MIT
Exploded Torus Fibrations
Holomorphic curves are powerfull tools in symplectic topology. In many cases,
information about holomorphic curves is obtained by considering a degenerating family
of complex structures. The category of exploded torus fibrations is an extension of the
category of smooth manifolds in which there is a good theory of holomorphic curves and some
of these degenerations are well behaved. I will give some examples and explain the relationship
of this with symplectic field theory and tropical geometry. 
October 13, 2006 10:35 AM  11:10 AM 
Rosa SenaDias, MIT/IST
Estimated Transversality and Rational Maps
In his work on symplectic Lefschetz pencils, Donaldson introduced the notion of
estimated transversality for a sequence of sections of a bundle. Together with
asymptotic holomorphicity, it is the key ingredient allowing the construction of
symplectic submanifolds. Despite its importance in the area, estimated transversality
has remained a mysterious property. The aim of this talk is to shed some light into this
notion by studying it in the simplest possible case namely that of S^{2}.
We state some new results about high degree rational maps on the 2sphere that can be seen
as consequences of Donaldson’s existence theorem for pencils, and explain how one might go
about answering a question of Donaldson: what is the best estimate for transversality that
can be obtained? We also show how the methods applied to S^{2} can be further
generalized. 
October 13, 2006 11:30 AM  12:05 PM 
Dagan Karp, Berkeley
The Cremona Transform in GromovWitten Theory
The Cremona transform is a classically studied rational map on projective space
P^{n}. It admits a resolution on X, an iterated toric blowup of
P^{n}. The space X possesses a symmetry which descends to the
theory of the blowup of P^{n} along only points, and hence to P^{n}
itself. This symmetry expresses some difficult to compute invariants in terms of others that
are easy to compute, and provides a new technique for the computation of these invariants
of P^{n}. Also, this recovers interesting enumerative results.

October 13, 2006 12:10 PM  12:45 PM 
Davesh Maulik, Princeton
GW/Hilb/DT Correspondence for A_{n} Resolutions
We explain the equivalence of the three theories described in the title for resolved
A_{n} singularities and discuss related questions and applications.
This is joint work with A. Oblomkov. 
 
Department of Mathematics, Stony Brook