Press and Dyson (2012) discovered a special set of strategies in two-player Iterated Prisoner's Dilemma games, the zero-determinant (ZD) strategies. Surprisingly, a player using such strategies can… (More)

We construct a desingularization of the “main component” M 0 1,k(P , d) of the moduli space M1,k(P , d) of genus-one stable maps into the complex projective space P. As a bonus, we obtain… (More)

In this paper we exploit the geometric approach to the virtual fundamental class, due to FukayaOno and Li-Tian, to compare the virtual fundamental classes of stable maps to a symplectic manifold and… (More)

In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror… (More)

We describe a natural isomorphism between the set of equivalence classes of pseudocycles and the integral homology groups of a smooth manifold. Our arguments generalize to settings well-suited for… (More)

We describe in detail a gluing construction for pseudoholomorphic maps in symplectic geometry, including in the presence of an obstruction bundle. The main motivation is to try to compare the… (More)

We compute the reduced genus-one Gromov-Witten invariants of Calabi-Yau hypersurfaces. As a consequence, we confirm the 1993 Bershadsky-Cecotti-Ooguri-Vafa (BCOV) prediction for the standard… (More)

We express the genus-two fixed-complex-structure enumerative invariants of P and P in terms of the genus-zero enumerative invariants. The approach is to relate each genus-two fixedcomplex-structure… (More)

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach is far more elementary than the “elementary” techniques of classical… (More)

We show that certain naturally arising cones over the main component of a moduli space of J0-holomorphic maps into P n have a well-defined euler class. We also prove that this is the case if the… (More)