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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Algebraic Structures from Integral Equations
积分方程 代数结构 代数分析
2023/11/29
Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Algebraic topology of digraphs and its applications
有向图 代数拓扑 图论
2023/11/15
High-order interaction occurs in various complex network, such as social network, bionetwork and network medicine. Comparing with that there are a lot of well-developed math tools (from graph theory) ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An algebraic framework for geometrically continuous splines
几何 连续样条 代数框架
2023/11/6
Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
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：Vanishing of some algebraic cycles on powers of Shimura curves
志村曲线 幂 代数 循环消失
2023/4/27
For a smooth projective variety over a number field, the Beilinson—Bloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Application of algebraic curve theory to integrable systems
代数曲线理论 可积系统 紧黎曼曲面
2023/5/5
We first consider the basic theory of algebraic curves, including the compact Riemann surface, Riemann-Hurwitz formula, Baker-Akhiezer function, three kinds of Abelian differentials, the construction ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On open subgroups of p-adic algebraic groups
p-adic 代数群 开子群
2023/5/5
In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The algebraic incarnations of the Artin Vanishing
Artin 消失 代数化身
2023/5/16
The non-abelian Hodge theory, briefly can be viewed as building a correspondence between certain topological objects, analytic objects, and algebraic objects. In this talk, I will show that Kodaira-ty...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Computations in equivariant algebraic topology
等变 代数拓扑 计算
2023/5/17
Modern algebraic topology sees equivariance arising in unexpected context. Equivariant cohomology carries rich structures but is much harder to compute. In 2009, Hill, Hopkins, and Ravenel solved the ...
Towards Instantiating the Algebraic Group Model
Public-key cryptography algebraic group model generic group model
2019/9/16
The Generic Group Model (GGM) is one of the most important tools for analyzing the hardness of a cryptographic problem. Although a proof in the GGM provides a certain degree of confidence in the probl...
Blind Schnorr Signatures in the Algebraic Group Model
Schnorr signatures blind signatures algebraic group model
2019/8/2
We study the security of schemes related to Schnorr signatures in the algebraic group model (AGM) proposed by Fuchsbauer, Kiltz, and Loss (CRYPTO 2018), where the adversary can only compute new group ...
Many cryptographic schemes have been proposed from learning with errors problems over some rings (Ring-LWE). Polynomial time quantum reduction from the approximating Shortest Independent Vectors Probl...
Improved Interpolation Attacks on Cryptographic Primitives of Low Algebraic Degree
Block cipher Cryptanalysis Interpolation attack
2019/7/15
Symmetric cryptographic primitives with low multiplicative complexity have been proposed to improve the performance of emerging applications such as secure Multi-Party Computation. However, primitives...
Algebraic Techniques for Short(er) Exact Lattice-Based Zero-Knowledge Proofs
Lattices Zero-Knowledge Proofs Commitments
2019/6/4
A key component of many lattice-based protocols is a zero-knowledge proof of knowledge of a vector s⃗ s→ with small coefficients satisfying As⃗ =u⃗ modqAs→=u→modq. While there exist ...