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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic mixed Siegel-Weil formulas and modular forms of arithmetic divisors
算术混合 西格尔-威尔公式 算术除数 模形式
2023/5/5
The classical Siegel–Weil formula relates theta series to Eisenstein series and its arithmetic version is central in Kudla's program. I will discuss arithmetic mixed Siegel-Weil formulas. I will focus...
Reduced Mumford divisors of a genus 2 curve through its jacobian function field
hyperelliptic Mumford arithmetic
2017/2/20
We explore the function field of the jacobian JH of a hyperelliptic curve H of genus 2 in order to find reduced coordinates to represent points of JH and do arithmetic. We show how this relates to the...
The QARMA Block Cipher Family -- Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes
Tweakable Block Ciphers Almost MDS Matrices Even-Mansour Schemes
2016/5/9
We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to ...
A New Algorithm for Solving the General Approximate Common Divisors Problem and Cryptanalysis of the FHE Based on the GACD problem
General approximate common divisors problems Fully homomorphic encryption Lattice
2016/1/26
In this paper, we propose a new algorithm for solving the general approximate common divisors (GACD) problems, which is based on lattice reduction algorithms on certain special lattices and linear equ...
Solving Linear Equations Modulo Unknown Divisors: Revisited
Lattice-based analysis Linear modular equations RSA
2016/1/9
We revisit the problem of finding small solutions to a collection
of linear equations modulo an unknown divisor p for a known
composite integer N. In CaLC 2001, Howgrave-Graham introduced an
effici...
Boundary Divisors in the Moduli Space of Stable Quintic Surfaces
algebraic geometry deformation theory moduli space
2014/12/8
I give a bound on which singularities may appear on KSBA stable surfaces for a wide range of topological invariants, and use this result to describe all stable numerical quintic surfaces, i.e. stable ...
Polyhedral Divisors, Dedekind Domains and Algebraic Function Fields
Polyhedral Divisors Dedekind Domains Algebraic Function Fields
2012/7/11
In this paper, we show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We describe also a class of multigraded a...
Approximate common divisors via lattices
foundations / Coppersmith's algorithm lattice basis reduction approximate common divisors
2012/3/26
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the $m$-variable case with modulus $N$ and approximate common divisor of size $...
Faster Algorithms for Approximate Common Divisors: Breaking Fully-Homomorphic-Encryption Challenges over the Integers
public-key cryptography / fully-homomorphic encryption cryptanalysis
2012/3/26
At EUROCRYPT '10, van Dijk, Gentry, Halevi and Vaikuntanathan presented simple fully-homomorphic encryption (FHE) schemes based on the hardness of approximate integer common divisors problems, which w...
$sl_2$ conformal block divisors and the nef cone of $\bar{M}_{0,n}$
the nef cone Algebraic Geometry
2011/9/21
Abstract: We show that $sl_2$ conformal block divisors do not cover the nef cone of $\bar{M}_{0,6}$, or the $S_9$-invariant nef cone of $\bar{M}_{0,9}$. A key point is to relate the nonvanishing of in...
A canonical linear system associated to adjoint divisors in characteristic $p > 0$
Linear system test ideal multiplier ideal base-point-free ample characteristic p > 0
2011/9/15
Abstract: Suppose that $X$ is a projective variety over an algebraically closed field of characteristic $p > 0$. Further suppose that $L$ is an ample (or more generally in some sense positive) divisor...
Abstract: In this paper we compute the pullback of divisor classes under the Prym map (extended to the boundary), and apply this result to get a lower bound on the slope of effective divisors on the p...
Homological algebra modulo exact zero-divisors
Exact zero divisors (co)homology complexity
2011/1/21
We study the homological behavior of modules over local rings modulo exact zero-divisors. We obtain new results which are in some sense “opposite” to those known for modules over local rings modulo re...
Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces
Abelian Yang-Mills theory Real tori Theta divisors
2010/11/11
The purpose of this paper is to determine natural theta line bundles of Klein surfaces as elements in the Grothendieck cohomology group which classifies Real line bundles in the sense of Atiyah. Thes...
Some conjectures on the maximal height of divisors of $x^n-1$
cyclotomic polynomials heights of polynomials
2010/12/14
Define B(n) to be the largest height of a polynomial in Z[x] dividing xn−1. We formulate a number of conjectures related to the value of B(n) when n is of a prescribed form. Additionally,we prov...