Abstracts
Mathieu Stiénon, Pennsylvania State University
Geometry of Maurer-Cartan elements on complex manifolds
Maurer-Cartan elements on a complex manifold are extensions of holomorphic Poisson structures. We study the geometry of these structures, by investigating their homology and cohomology theory. In particular, we describe a duality on the homology groups, which generalizes the Serre duality of Dolbeault cohomology.
Ho Hon Leung, Cornell University
Divided difference operators in Kasparov's equivariant KK-theory
Let $G$ be a compact connected Lie group with maximal torus $T$. Let $A$, $B$ be $G$-$C^\ast$-algebras. We define certain divided difference operators on Kasparov's $T$-equivariant KK-group $KK_T(A,B)$ and show that $KK_G(A,B)$ is a direct summand of $KK_T(A,B)$. More precisely, a $T$-equivariant KK-class is $G$-equivariant if and only if it is annihilated by an ideal of divided difference operators. This result is a generalization of work done by Atiyah, and Harada, Landweber and Sjamaar. The talk will include a brief introduction to Kasparov's KK-theory.
Yael Karshon, University of Toronto
Symplectic blowups of the complex projective plane, and counting torus actions
In how many different ways can a two-torus act on a given simply connected symplectic four-manifold?
If the second Betti number is one or two, this was known. If the second Betti number is three or more, to reduce the question to combinatorics, we describe the manifold as a symplectic blowup in a way that is compatible with all the torus actions simultaneously. For this we use the theory of pseudoholomorphic curves.
This is joint work with Liat Kessler and Martin Pinsonnault.
Victor Batyrev, Universität Tübingen
Kähler metrics on spherical varieties
The talk is devoted to some generalizations of ideas used in constructing special Kähler metrics on toric varieties to the case of spherical varieties.