# Past Algebraic and Symplectic Geometry Seminar

20 May 2008
14:15
Thomas Nevins
Abstract
• Algebraic and Symplectic Geometry Seminar
13 May 2008
15:45
Diane Maclagan
Abstract
• Algebraic and Symplectic Geometry Seminar
6 May 2008
15:45
Alastair King
Abstract
I plan to discuss some aspects the mysterious relationship between the symmetries of toroidal compactifications of M-theory and helices on del Pezzo surfaces.
• Algebraic and Symplectic Geometry Seminar
29 April 2008
15:45
Ben McKay
Abstract
• Algebraic and Symplectic Geometry Seminar
22 April 2008
15:45
Miles Reid
Abstract
• Algebraic and Symplectic Geometry Seminar
4 March 2008
14:45
• Algebraic and Symplectic Geometry Seminar
26 February 2008
14:45
Raphael Rouquier
Abstract
• Algebraic and Symplectic Geometry Seminar
12 February 2008
14:45
Abstract
Let G be a connected reductive algebraic group over an algebraically closed field of characteristic 0. A normal irreducible G-variety X is called spherical if a Borel subgroup of G has an open orbit on X. It was conjectured by F. Knop that two smooth affine spherical G-varieties are equivariantly isomorphic provided their algebras of regular functions are isomorphic as G-modules. Knop proved that this conjecture implies a uniqueness property for multiplicity free Hamiltonian actions of compact groups on compact real manifolds (the Delzant conjecture). In the talk I am going to outline my recent proof of Knop's conjecture (arXiv:math/AG.0612561).
• Algebraic and Symplectic Geometry Seminar
5 February 2008
14:45
Mohammed Abouzaid
Abstract
• Algebraic and Symplectic Geometry Seminar
29 January 2008
14:45
Dominic Joyce
Abstract
This is the second of two talks, and probably will not be comprehensible unless you came to last week's talk. A Kuranishi space is a topological space equipped with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on many moduli spaces in differential geometry, and in particular, in moduli spaces of stable $J$-holomorphic curves in symplectic geometry. Let $Y$ be an orbifold, and $R$ a commutative ring. We define four topological invariants of $Y$: two kinds of Kuranishi bordism ring $KB_*(Y;R)$, and two kinds of Kuranishi homology ring $KH_*(Y;R)$. Roughly speaking, they are spanned over $R$ by isomorphism classes $[X,f]$ with various choices of relations, where $X$ is a compact oriented Kuranishi space, which is without boundary for bordism and with boundary and corners for homology, and $f:X\rightarrow Y$ is a strong submersion. These theories are powerful tools in symplectic geometry. Today we discuss the definition of Kuranishi homology, and the proof that weak Kuranishi homology is isomorphic to the singular homology.
• Algebraic and Symplectic Geometry Seminar