12 citations · 13 across the 9 of their papers we have counts for
9 papers
Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms
Dingxin Zhang, Jie Zhou
We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are com…
Exponentially twisted de Rham cohomology and rigid cohomology
Shizhang Li, Dingxin Zhang
We prove a comparison theorem between exponentially twisted de Rham cohomology and rigid cohomology with coefficients in a Dwork crystal.
Mixed Hodge structure and Coulomb branch solution
Dan Xie, Dingxin Zhang
The Coulomb branch of four dimensional theories can be solved by finding a Seiberg-Witten (SW) geometry and a SW differential. While lots of SW geometries are found…
-adic Tautological Systems
Lei Fu, An Huang, Bong Lian +3
Tautological systems was introduced in Lian-Yau as the system of differential equations satisfied by period integrals of hyperplane sections of some complex projective homogenous v…
On Vlasenko's formal group laws
Dingxin Zhang
Given a Laurent polynomial over a ring flat over \(\mathbb{Z}\), Vlasenko defines a formal group law. We identify this formal group law with a coordinate system of a formal group f…
On a conjecture of Huang--Lian--Yau--Yu
Tsung-Ju Lee, Bong Lian, Dingxin Zhang
We verify a formula on the solution rank of the tautological system arising from ample complete intersections in a projective homogeneous space of a semisimple group conjectured by…
The Monsky--Washnitzer topos
Dingxin Zhang
Mimicking Ogus's construction, we define a site, for varieties over a field of char. p > 0, using Monsky--Washnitzer algebras/weak formal schemes. We prove a comparison theorem bet…
-hypergeometric systems and relative cohomology
Tsung-Ju Lee, Dingxin Zhang
We investigate the space of solutions to certain -hypergeometric -modules, which were defined and studied by Gelfand, Kapranov, and Zelevinsky. We show that the sol…
Automorphism and Cohomology II: Complete intersections
Xi Chen, Xuanyu Pan, Dingxin Zhang
We prove that the automorphism group of a general complete intersection in a projective space is trivial with a few well-understood exceptions. We also prove that the automorph…