On Thursday May 6th, Grigory Mikhalkin and Jaroslaw Wlodarczyk will speak in the Cambridge COW algebraic geometry seminar. Talks will be held in Meeting Room 13 in the Centre for Mathematical Sciences, Clarkson Road, Cambridge, with pub/dinner afterward. Everyone is welcome!
More details, including how to claim travel expenses, are available from the COW website: here.
Thursday 6th May
2.30pm: Grigory Mikhalkin (Geneva). Tropical (p,q)-cycles.
4.30pm: Jaroslaw Wlodarczyk (Purdue). Resolution algorithm in characteristic zero and its possible extension to positive characteristic.
Real 1-parametric families of complex manifolds have limits collapsing to certain polyhedral complexes called tropical varieties. Tropical structure of these limits is responsible for asymptotics of the collapse.
Tropical varieties are simple enough to visualize easily. Yet their homology theories reflect the Hodge structure of the collapsing family. These theories agree with the classical mixed Hodge structures in the case when the real 1-parametric families can be extended to the complex domain.
The talk will review some basic tropical notions and will be illustrated with a few examples.
We discuss the basic ideas of the Hironaka algorithm for the resolution of singularities of algebraic varieties in characteristic zero and its extension to positive characteristic.