Related papers: Effective computations of the Atiyah-Bott formula
The main goal of the paper is to present a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves. A secondary goal is to present an exposition of the circle of…
We characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, anti-holomorphic involution, then the…
The abelian-nonabelian correspondence outlined by Bertram, Ciocan-Fontanine, and Kim gives a broad conjectural relationship between (twisted) Gromov-Witten invariants of related GIT quotients. This paper proves a case of the correspondence…
We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over $\mathbb Q$, and we show how to use it to compute regulators for a number of Jacobians of smooth…
The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…
The elliptic quasimap potential function is explicitly calculated for Calabi-Yau complete intersections in projective spaces by Kim and Lho. We extend this result to local Calabi-Yau varieties. Using this as well as the wall crossing…
We study the Horn problem in the context of algebraic codes on a smooth projective curve defined over a finite field, reducing the problem to the representation theory of the special linear group $SL(2,F_q)$. We characterize the…
Let F be the complete flag variety over Spec(Z) with the tautological filtration 0 \subset E_1 \subset E_2 \subset ... \subset E_n=E of the trivial bundle E over F. The trivial hermitian metric on E(\C) induces metrics on the quotient line…
Using the associativity relations of the topological Sigma Models with target spaces, $CP^3, CP^4$ and $Gr(2,4)$ , we derive recursion relations of their correlation and evaluate them up to certain order in the expansion over the…
G\"ottsche-Schroeter invariants are a genus 0 extension of Block-G\"ottsche invariants. They interpolate between Welschinger invariants involving pairs of complex conjugated points and genus 0 descendant Gromov-Witten invariants. They can…
The first part of this work constructs real positive-genus Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the second part studies the orientations on the moduli spaces of real maps used in…
Motivated by the work of Vishik on the analytic torsion we introduce a new class of generalized Atiyah-Patodi-Singer boundary value problems. We are able to derive a full heat expansion for this class of operators generalizing earlier work…
We compute the local Gromov-Witten invariants of certain configurations of rational curves in a Calabi-Yau threefold. These configurations are connected subcurves of the `minimal trivalent configuration', which is a particular tree of P^1's…
We compute certain open Gromov-Witten invariants for toric Calabi-Yau threefolds. The proof relies on a relation for ordinary Gromov-Witten invariants for threefolds under certain birational transformation, and a recent result of Kwokwai…
We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to…
For smooth complete intersections in the projective spaces, we use the deformation invariance of Gromov-Witten invariants and results in classical invariant theory to study the symmetric reduction of the WDVV equation by the monodromy…
We compute the $g=1, n=1$ B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category D(E). More precisely, we carry out the computation of the categorical Gromov-Witten invariant defined by Costello using as…
We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential…
We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe…
We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of…