Workshop Schedule (Preliminary)
May 7, 10-11, Vincent 207
Silvia Anjos, IST, Lisbon
Title: Some results on the homotopy type of symplectomorphism groups.
Abstract: By a result of Kedra and Pinsonnault, we know that the topology of groups
of symplectomorphisms of symplectic 4-manifolds is complicated in general, although,
in most of all known examples, the rational cohomology rings of these groups are finitely
generated. In this talk we compute the homotopy Lie algebra of groups of symplectomorphisms
of some 3-point and 4-point blow-ups of the projective plane and show it is infinite dimensional.
Nevertheless, the full topology of these groups can be understood: we show it is determined by
compact subgroups arising from Hamiltonian group actions. We also discuss some applications
to more blow-ups. Part of this work is joint with Martin Pinsonnault and Sinan Eden.
May 7, 1:30-2:30, Vincent 570
Jun Li, University of Michigan
Title: Symplectic $-2$ spheres and the Symplectomorphism group
Abstract:
Let $(X,\omega)$ be a symplectic rational surface. We study the space
of tamed almost complex structures $\mathcal{J}_{\omega}$ using a fine decomposition via smooth
rational curves and a relative version of the infinite dimensional Alexander
duality. This decomposition provides new understandings of both the variation
and stability of the symplectomorphism group $Symp (X,\omega) $ when deforming $\omega$.
In particular, we compute $\pi_1(Symp (X,\omega)) $ with $\chi(X) \leq 7$ in terms
of the number $N_{\omega}$ of $-2$ symplectic sphere classes. This is a joint work with Tian-Jun Li.
May 8, 10-11, Vincent 207
Anar Akhmedov, University of Minnesota
Title: New symplectic 4-manifolds with b+ = 1, 3
Abstract: We will discuss the topology of symplectic 4-manifolds with b+= 1, 3 and provide various constructions of symplectic 4-manifolds and Lefschetz fibrations with b+2 = 1 and prescribed c21.
This talk is based on two separate joint works Weiyi Zhang and Naoyuki Monden.
May 8, 2:30-3:30, Vincent 570
Martin Pinsonnault, University of Western Ontario
Title: Compact group actions on small symplectic rational surfaces
May 9, 11:30-12:30, Vincent 207
Ke Zhu, Minnesota State University, Mankato
Title: Solvability of Dirac type equations and automatic transversality of holomorphic curves
Abstract: Abstract: We develop a weighted L2-method for the (half)-Dirac equation. For Dirac bundles over Riemann surfaces, we give a sufficient condition for the solvability of the Dirac equation in terms of a curvature integral. Applying this to the Dolbeault-Dirac operator,
we establish an automatic transversality criteria for holomorphic curves in Kahler manifolds.
May 9, 2:00-3:00, Vincent 570
Weiwei Wu, University of Georgia
Title: Symplectomorphism group of CP2#5(-CP2)
May 10, 10-11, Vincent 207
Josef Dorfmeister, North Dakato State University
Title: Negative Curve Classes in Rational Manifolds
Abstract: Embedded symplectic curves in rational manifolds with negative self-intersection are of interest in numerous surgeries and conjectures. They are rather hard to construct in general. This talk will focus on describing those negative square classes with the potential to be represented by a symplectic curve in a rational symplectic manifold.
(Joint w. T.-J. Li and W. Wu.)
May 10, 1:30-2:30, Vincent 570
Xiliang Wang, University of Minnesota
Title: Minimal G-ruled surfaces
May 11, 9:30-10:30, Vincent 207
Sumeyra Sakalli, University of Minnesota
Title: Deformation of Singular Fibers of Genus 2 Fibrations and Small Exotic Symplectic 4-Manifolds
Abstract: In 1963, Kodaira classified all singular fibers in pencils of elliptic curves, and showed that in such a pencil, each fiber is either an elliptic curve or a rational curve with a node or a cusp, or a sum of rational curves of self-intersection -2. Later Namikawa and Ueno gave geometric classification of all singular fibers in pencils of genus two curves. In this talk, I will give topological constructions of certain singularity types in the Namikawa-Ueno¡¯s list. I will also discuss 2-nodal spherical deformation of certain singular fibers of genus two fibrations. Then by using them I will provide constructions of exotic, minimal, symplectic 4-manifolds homeomorphic but not diffeomorphic to
CP2#6(-CP2), CP2#7(-CP2) and 3CP2#k(-CP2) for k = 16,...,19. This is a joint work with Anar Akhmedov.
May 11, 10:40-11:40, Vincent 207
Tian-Jun Li, University of Minnesota
Symplecti log Calabi-Yau pairs