Speaker: Sergey Galkin

Title: On algebraic and arithmetic "quantum" invariants of Fano varieties

Date: Dec 22, 2008, 16:30 - 17:30

Place: Freie Universitaet, Berlin

Abstract:

We will discuss two invariants of (the strains of) Fano varieties derived from the quantum cohomology - the spectra and the Apery class. Former is the set of the roots of quantum characteristic polynomial, while the latter is the nonhomogeneous primitive cohomology class with interesting coefficients like zeta(5)-zeta(2)zeta(3). Besides basic properties of these invariants we will state the conjectures on their behaviour and provide some evidences for them - a theoretical computation for the Grassmannians (a cyclotomic formula for the spectra and an approximation to zeta(2)) and the experimental computations for other homogeneous spaces.