Talk

A 19th century problem in algebraic geometry is to understand the relation between the genus and the degree of a curve in complex projective space. This is easy in the case of the projective plane, but becomes quite involved already in the case of three dimensional projective space. I will talk about generalizing classical results on this problem by Gruson and Peskine to other threefolds. This includes principally polarized abelian threefolds of Picard rank one and some Fano threefolds.

I give a formulation of quantum theory where the starting point is a convex set of states. I show that
the formulas for probabilities can be derived from first principles.  One can define particles as
elementary excitations of ground state and quasiparticles as elementary excitations of translation invariant stationary state. The collisions of (quasi)particles  in the geometric approach are described by  inclusive scattering matrix.  (Inclusive cross-sections can be expressed in terms of inclusive scattering matrix. Only

Given a lattice polytope P, one can construct a toric variety X, together with an ample line bundle L on X. It turns out that its Euler characteristic is equal to the number of lattice points contained in P. Moreover, the Hirzebruch–Riemann–Roch theorem tells us how to calculate this Euler characteristic in terms of the Todd class of the toric variety X. This yields an efficient method for counting the lattice points in P, because there is a polynomial time algorithm that computes the Todd class of X given the polytope P.