Related papers: Topological recursion and mirror curves
We revisit the low-energy effective $U(1)$ action of topologically twisted $\mathcal N=2$ SYM theory with gauge group of rank one on a generic oriented smooth 4-manifold $X$ with nontrivial fundamental group. After including a specific new…
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive…
We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomorphic curves are generically…
We describe generating functions for arbitrary-genus Gromov-Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing…
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal…
We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of…
In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail…
I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of…
In a recent work [1] we consider the topological expansion for the non-mixed observables (including the free energy) for the formal Cauchy matrix model. The only restriction in [1] was the fact that all the branch points have to be simple.…
We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are…
We study the free product of rooted graphs and its various decompositions using quantum probabilistic methods. We show that the free product of rooted graphs is canonically associated with free independence, which completes the proof of the…
We derive a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds and verify the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa.
We propose Picard-Fuchs equations for periods of nonabelian mirrors in this paper. The number of parameters in our Picard-Fuchs equations is the rank of the gauge group of the nonabelian GLSM, which is eventually reduced to the actual…
An analogy is drawn between recent work with Kley (math.AG/0007082) and the WDVV equations. That is, both are regarded as symmetries of generating functions with coefficients that "count" rational curves on a complex projective manifold. It…
We deduce the constraint structure and subsequently quantize a free particle system residing on a torus satisfying the geometric constraint $(r-a)=0$, within the framework of modified Faddeev-Jackiw formalism. Further, we reformulate the…
Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic curves, i.e., a statement relating certain labeled…
We consider certain families of Calabi-Yau orbifolds and their mirror partners constructed from Fermat hypersurfaces in weighted projective 4-spaces. Our focus is the topological mirror symmetry. There are at least three known ingredients…
We introduce a global Landau-Ginzburg model which is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum…
By studying the weak closure of multidimensional off-diagonal self-joinings we provide a criterion for non-isomorphism of a flow with its inverse, hence the non-reversibility of a flow. This is applied to special flows over rigid…
A tropical curve in $\mathbb R^{3}$ contributes to Gromov-Witten invariants in all genus. Nevertheless, we present a simple formula for how a given tropical curve contributes to Gromov-Witten invariants when we encode these invariants in a…