As part of the Dusafest conference, on the morning of Friday Oct 13, there will be a mini-workshop consisting of five 35-minute talks by young researchers. The mini-workshop will also be held in S-240, in the basement of the Math Building. Coffee and other refreshments will be available, and a light breakfast will be served in the morning.


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 Morse-Smale. 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 Sena-Dias, 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 S2. We state some new results about high degree rational maps on the 2-sphere 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 S2 can be further generalized.

October 13, 2006
11:30 AM - 12:05 PM
Dagan Karp, Berkeley
The Cremona Transform in Gromov-Witten Theory

The Cremona transform is a classically studied rational map on projective space Pn. It admits a resolution on X, an iterated toric blowup of Pn. The space X possesses a symmetry which descends to the theory of the blowup of Pn along only points, and hence to Pn 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 Pn. Also, this recovers interesting enumerative results.

October 13, 2006
12:10 PM - 12:45 PM
Davesh Maulik, Princeton
GW/Hilb/DT Correspondence for An Resolutions

We explain the equivalence of the three theories described in the title for resolved An singularities and discuss related questions and applications. This is joint work with A. Oblomkov.

Department of Mathematics, Stony Brook