10 papers
Simple singularities and integrable hierarchies
Alexander B. Givental, Todor E. Milanov
The paper math.AG/0108100 gives a construction of the total descendent potential corresponding to a semisimple Frobenius manifold. In math.AG/0209205, it is proved that the total d…
Symplectic geometry of Frobenius structures
Alexander Givental
The purpose of the notes is to reiterate and expand the viewpoint, outlined in the paper math.AG/0110142 of T. Coates and the author, which recasts the concept of Frobenius manifol…
A_{n-1} singularities and nKdV hierarchies
Alexander Givental
According to a conjecture of E. Witten proved by M. Kontsevich, a certain generating function for intersection indices on the Deligne -- Mumford moduli spaces of Riemann surfaces c…
Quantum Riemann - Roch, Lefschetz and Serre
Tom Coates, Alexander Givental
Given a holomorphic vector bundle over a compact Kähler manifold, one introduces twisted GW-invariants of replacing virtual fundamental cycles of moduli spaces of stab…
Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups
Alexander Givental, Yuan-Pin Lee
We conjecture that appropriate K-theoretic Gromov-Witten invariants of complex flag manifolds G/B are governed by finite-difference versions of Toda systems constructed in terms of…
Gromov - Witten invariants and quantization of quadratic hamiltonians
Alexander B. Givental
We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and…