Super-rigidity and finiteness of embedded $J$-holomorphic curves on Calabi-Yau threefolds

Automorphism group of Batyrev Calabi-Yau threefolds

In this paper, we will prove that all Batyrev Calabi-Yau threefolds, arising from a small resolution of a generic hyperplane section of a reflexive Fano-Gorenstein fourfold, have finite automorphism group. Together with Morrison conjecture, this suggests that Batyrev Calabi-Yau threefolds should have a polyhedral Kahler (ample) cone.

A relation for Gromov-Witten invariants of local Calabi-Yau threefolds

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 Chan.

conifold与局部Calabi-Yau三维流形上的Poisson结构

Poisson structures on the conifold and local Calabi-Yau threefolds

本文研究了局部Calabi-Yau三维流形上的双向量场与Poisson结构，并计算了conifold上所有可能的全纯Poisson结构。

Real Lagrangians in Calabi-Yau Threefolds

We compute the mod $2$ cohomology groups of real Lagrangians in Calabi-Yau threefolds using well-behaved torus fibrations constructed by Gross. To do this we study a long exact sequence introduced by Castaño-Bernard and Matessi, which relates the cohomology of the Lagrangians to the cohomology of the Calabi-Yau. We show that the connecting homomorphism in this sequence is given by the map squaring divisor classes in the mirror Calabi-Yau.

A Note on Schoen's Calabi--Yau Threefolds

We study the topology of a real Lagrangian in Schoen's Calabi--Yau threefold $X$ and compute its mod $2$ cohomology using two methods; first via a concrete Mayer--Vietoris calculation, then by an exact sequence relating the mod $2$ cohomology of the real Lagrangian to the cohomology of $X$. We conclude that these two methods agree. This in particular corrects a previous computation made by Castaño-Bernard--Matessi.

On Emergent Geometry of the Gromov-Witten Theory of Quintic Calabi-Yau Threefold

We carry out the explicit computations that are used to write down the integrable hierarchy associated with the quintic Calabi-Yau threefold. We also do the calculations for the geometric structures emerging in the Gromov-Witten theory of the quintic, such as the Frobenius manifold structure and the special Kähler structure.