52 citations · 96 across the 22 of their papers we have counts for
25 papers
Quadratic reciprocity from a family of adelic conformal field theories
An Huang, Bogdan Stoica, Xiao Zhong
We consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized f…
Massless -brane modes and the critical line
An Huang, Bogdan Stoica, Xiao Zhong
We consider a -brane model as a theory of maps from the vertices of the Bruhat-Tits tree times into . We show that in order for the worldsheet time e…
-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…
Bounds on the Ricci curvature and solutions to the Einstein equations for weighted graphs
An Huang, Bogdan Stoica, Xuyang Xia +1
This is a preliminary study of the equation of motion of Euclidean classical gravity on a graph, based on the Lin-Lu-Yau Ricci curvature on graphs. We observe that the constant edg…
From -adic to Archimedean Physics: Renormalization Group Flow and Berkovich Spaces
An Huang, Dan Mao, Bogdan Stoica
We introduce the -adic particle-in-a-box as a free particle with periodic boundary conditions in the -adic spatial domain. We compute its energy spectrum, and show that the s…
On the Sum of Ricci-Curvatures for Weighted Graphs
Shuliang Bai, An Huang, Linyuan Lu +1
In this paper, we generalize Lin-Lu-Yau's Ricci curvature to weighted graphs and give a simple limit-free definition. We prove two extremal results on the sum of Ricci curvatures f…
Green's Functions for Vladimirov Derivatives and Tate's Thesis
An Huang, Bogdan Stoica, Shing-Tung Yau +1
Given a number field with a Hecke character , for each place we study the free scalar field theory whose kinetic term is given by the regularized Vladimirov derivative a…
Existence of Solutions to Mean Field Equations on Graphs
An Huang, Yong Lin, Shing-Tung Yau
In this paper, we prove two existence results of solutions to mean field equations and on an arbitrary connected finit…
General relativity from -adic strings
An Huang, Bogdan Stoica, Shing-Tung Yau
For an arbitrary prime number , we propose an action for bosonic -adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a con…
Jacobian rings for homogenous vector bundles and applications
An Huang, Bong Lian, Shing-Tung Yau +1
In this note, we examine the Jacobian ring description of the Hodge structure of zero loci of vector bundle sections on a class of ambient varieties. We consider a set of cohomolog…
Period integrals of local complete intersections and tautological systems
An Huang, Bong Lian, Shing-Tung Yau +1
Tautological systems developed in [6],[7] are Picard-Fuchs type systems to study period integrals of complete intersections in Fano varieties. We generalize tautological systems to…
Hasse-Witt matrices, unit roots and period integrals
An Huang, Bong Lian, Shing-Tung Yau +1
Motivated by the work of Candelas, de la Ossa and Rodriguez-Villegas [6], we study the relations between Hasse-Witt matrices and period integrals of Calabi-Yau hypersurfaces in bot…
Differential zeros of period integrals and generalized hypergeometric functions
Jingyue Chen, An Huang, Bong H. Lian +1
In this paper, we study the zero loci of local systems of the form , where is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space ,…
Holonomic Systems for Period Mappings
Jingyue Chen, An Huang, Bong H. Lian
Period mappings were introduced in the sixties [G] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced re…
Chain Integral Solutions to Tautological Systems
An Huang, Bong H. Lian, Shing-Tung Yau +1
We give a new geometrical interpretation of the local analytic solutions to a differential system, which we call a tautological system , arising from the universal family of Cal…
On cohomology theory of (di)graphs
An Huang, Shing-Tung Yau
To a digraph with a choice of certain integral basis, we construct a CW complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph…
Graph invariants from ideas in physics and number theory
An Huang, Shing-Tung Yau, Mei-Heng Yueh
We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a…
Period Integrals and the Riemann-Hilbert Correspondence
An Huang, Bong H. Lian, Xinwen Zhu
A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete inter…
On the Holonomic Rank Problem
Spencer Bloch, An Huang, Bong H. Lian +2
A tautological system, introduced in \cite{LSY}\cite{LY}, arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of com…
Period Integrals and Tautological Systems
Bong H. Lian, Ruifang Song, Shing-Tung Yau
We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of re…
Noncommutative multiplicative norm identities for the quaternions and the octonions
An Huang
We present Capelli type identities associated with the quaternions and the octonions, which are noncommutative versions of multiplicative norm identities for the quaternions and th…
Simplifying Local BRST Cohomology Calculation via Spectral Sequence
An Huang
We simplify some crucial calculations in \cite{1} by using the technique of spectral sequence of a double complex.
A Note on Nahm's Conjecture in Rank 2 Case
An Huang, Chul-hee Lee
The aim of this paper is to get a complete list of positive definite symmetric matrices with integer entries $\a&b\b&d$ such that all complex solutions to the system of equations…
On S-duality and Gauss reciprocity law
An Huang
We review the interpretation of Tate's thesis by a sort of conformal field theory on a number field in \cite{1}. Based on this and the existence of a hypothetical 3-dimensional gau…