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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
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2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Non-abelian Derived Categories and Derived Schur and Weyl Functors
非阿贝尔派生范畴 派生舒尔 外尔函子
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2023/4/13
We'll start with reviewing Quillen and Lurie's theory of non-abelian derived categories (also known as the "animation" theory). Following that, we will apply this theory to generalize the classical Sc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fourier analysis on finite abelian groups and the uncertainty principles
有限阿贝尔群 傅里叶分析 不确定性原理
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2023/4/18
Let G be a finite abelian group. If f: G → C is a nonzero function with Fourier transform f , the Donoho-Stark uncertainty principle states that|supp(f)||supp(f )|≥|G|. The purpose of this talk is two...
On Abelian Secret Sharing: duality and separation
Access structure Duality Characteristic-dependent information ratio
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2019/5/29
Unlike linear secret sharing, very little is known about abelian secret sharing. In this paper, we present two results on abelian secret sharing. First, we show that the information ratio of access st...
具有蝴蝶型相图的三次近Hamilton系统Abelian积分的零点个数
Hamilton系统 Abelian积分 Picard-Fuchs方程 蝴蝶型相图
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2018/3/9
具有蝴蝶型相图的三次近Hamilton系统Abelian积分的零点个数。
Impossibility of Secure Multi-Party Products in Non-Abelian Groups
foundations mpc
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2017/7/19
Suppose nn parties have respective inputs x1,…,xn∈Gx1,…,xn∈G, where GG is a finite group. The parties would like to privately compute x1x2⋯xnx1x2⋯xn (where multiplication refers to the gro...
Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography
elliptic curve cryptosystem number theory
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2017/5/5
We call a simple abelian variety over FpFp super-isolated if its (FpFp-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about iso...
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Isogeny expander graph hyperelliptic curve cryptography
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2017/2/20
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multip...
Isogeny graphs of ordinary abelian varieties
Jacobians of hyperelliptic curves genus 2 cryptography isogeny graphs
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2016/12/8
Fix a prime number ГГ. Graphs of isogenies of degree a power of ГГ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ord...
Proposal for observing non-Abelian statistics of Majorana-Shockley fermions in an optical lattice
non-Abelian statistics Majorana-Shockley fermions an optical lattice
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2016/1/22
Besides the conventional bosons and fermions, in synthetic two-dimensional (2D) materials there could exist more exotic quasiparticles with non-Abelian statistics, meaning that the quantum states in t...
Constructing Abelian Surfaces for Cryptography via Rosenhain Invariants
hyperelliptc curves complex multiplication Rosenhain invariants
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2016/1/9
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their
Kummer surfaces via Rosenhain invariants and related Kummer parameters. The most common
version of the...
Arithmetic on Abelian and Kummer Varieties
foundations Arithmetic Kummer Varieties
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2016/1/8
A Kummer variety is obtained as the quotient of an abelian variety by the automorphism
(−1) acting on it. Kummer varieties can be seen as a higher dimensional generalisation of the xcoordinate
...
Non-Abelian Analogs of Lattice Rounding
lattice rounding matrix groups norm concentration
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2016/1/5
Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of...
SOME REMARKS ON THE LOGARITHMIC SIGNATURES OF FINITE ABELIAN GROUPS
logarithmic signatures quasi-logarithmic signatures cyclic 2-group
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2015/12/22
In the paper about the cryptosystem MST3, Svaba and Trung proposed
a way to build a cryptosystem based on the concept of logarithmic signatures,
and they choose Suzuki’s group, which is not abelian ...
Pseudo-Free Families of Finite Computational Elementary Abelian p-Groups
collision-intractable family of functions one-way family of functions family of p-ary hash functions
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2015/12/21
We initiate the study of (weakly) pseudo-free families of computational elementary abelian pgroups,
where p is an arbitrary fixed prime. We restrict ourselves to families of computational
elementary...