38 citations · 100 across the 7 of their papers we have counts for
8 papers · 1 filter
K-theoretic Gromov--Witten invariants in genus 0 and integrable hierarchies
Todor Milanov, Valentin Tonita
We prove that the genus-0 invariants in K-theoretic Gromov--Witten theory are governed by an integrable hierarchy of hydrodynamic type. If the K-theoretic quantum product is semisi…
A formula for the total permutation-equivariant K-theoretic Gromov-Witten potential
Valentin Tonita
We give a summation over graphs type formula for the permutation-equivariant K-theoretic Gromov-Witten total potential of a projective manifold X in terms of cohomological Gromov-W…
Twisted K-theoretic Gromov-Witten invariants
Valentin Tonita
We introduce twisted K-theoretic Gromov-Witten invariants - in the frameworks of both "ordinary" and permutation-equivariant K-theoretic GW theory defined recently by Givental. We…
Reconstruction and Convergence in Quantum -Theory via Difference Equations
Hiroshi Iritani, Todor Milanov, Valentin Tonita
We give a new reconstruction method of big quantum -ring based on the -difference module structure in quantum -theory. The -difference structure yields commuting linear…
Quantum orbifold Hirzebruch-Riemann-Roch theorem in genus zero
Valentin Tonita, Hsian-Hua Tseng
We introduce K-theoretic Gromov-Witten invariants of algebraic orbifold target spaces. Using the methods developed by Givental-Tonita we characterize Giventals Lagrangian cone of q…
Twisted orbifold Gromov-Witten invariants
Valentin Tonita
Let $\ix$ be a smooth Deligne-Mumford stack over the complex numbers. One can define twisted orbifold Gromov-Witten invariants of $\ix$ by considering multiplicative invertible cha…
A virtual Kawasaki formula
Valentin Tonita
Kawasaki's formula is a tool to compute holomorphic Euler characteristics of vector bundles on a compact orbifold X. Let X be an orbispace with perfect obstruction theory which adm…
The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory
Alexander Givental, Valentin Tonita
We completely characterize genus-0 K-theoretic Gromov-Witten invariants of a compact complex algebraic manifold in terms of cohomological Gromov-Witten invariants of this manifold.…