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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Modularity of WRT invariants via resurgence theory
复活理论 WRT不变量 模性
2023/11/29
We will talk about the (quantum) modularity of WRT invariants or GPPV invariants in general of Seifert fibered homology spheres. It turns out that they are related to the Stokes phenomena of the Ohtsu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Futaki invariants and Yau’s conjecture on the Hull-Strominger system
Futaki invariants 丘成桐 赫尔-斯特罗明格系统 猜想
2023/4/23
In this talk, we will talk about Fernandez-Molina’s paper”Futaki invariants and Yau’s conjecture on the Hull-Strominger system”. We will introduce a new obstruction to the existence of solutions of th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Conformally variational Riemannian invariants and their related topics
共形变分 黎曼不变量 主题
2023/4/23
It is well known that scalar curvature plays a fundamental role in general relativity. As its analogue, conformally variational Riemannian invariants (CVIs) is a category of fundamental scalar-type cu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The definable content of homological invariants
同调 不变量 可定义内容
2023/5/15
In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "...
On the Existence of Non-Linear Invariants and Algebraic Polynomial Constructive Approach to Backdoors in Block Ciphers
block ciphers Boolean functions Algebraic Normal Form
2018/11/19
In this paper we study cryptanalysis with non-linear polynomials cf. Eurocrypt’95 (adapted to Feistel ciphers at Crypto 2004). Previously researchers had serious difficulties in making such attacks wo...
Block Cipher Invariants as Eigenvectors of Correlation Matrices
invariant subspace attack nonlinear invariant attack linear cryptanalysis
2018/8/21
A new approach to invariant subspaces and nonlinear invariants is developed. This results in both theoretical insights and practical attacks on block ciphers. It is shown that, with minor modification...
From Kantian schematism to the system of experience’s invariants:the coordination of concepts and spatio-temporal objects in Cassirer’s philosophy
Cassirer Kant concept schema object causality
2016/5/31
This paper analyzes Cassirer's account of the coordination of concepts and spatio-temporal objects. We shall see that, in contradistinction to Kantian schematism, Cassirer maintains that this coordina...
Symbolic Heap Abstraction with Demand-Driven Axiomatization of Memory Invariants
Heap Analysis Relational Static Analysis Array Analysis Memory Invariants
2016/5/24
Many relational static analysis techniques for precise reasoning about heap contents perform an explicit case analysis of all possible heaps that can arise. We argue that such precise relational reaso...
We describe a Guess-and-Check algorithm for computing algebraic equation invariants of the form ∧ifi(x1, . . . , xn) = 0, where each fi is a polynomial over the variables x1, . . . , xn of the program...
Constructing Abelian Surfaces for Cryptography via Rosenhain Invariants
hyperelliptc curves complex multiplication Rosenhain invariants
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...
We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a
two-step °ag variety. We also give symplectic and orthogonal...
GROMOV-WITTEN INVARIANTS AND QUANTUM COHOMOLOGY OF GRASSMANNIANS
GROMOV-WITTEN INVARIANTS QUANTUM COHOMOLOGY
2015/12/17
This is the written version of my ˉve lectures at the Banach Center
mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
THE RING OF PROJECTIVE INVARIANTS OF EIGHT POINTS ON THE LINE VIA REPRESENTATION THEORY
PROJECTIVE INVARIANTS EIGHT POINTS ON THE LINE VIA
2015/10/14
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular...
THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE:INTEGRALITY RESULTS
RELATIONS FOR THE RING INVARIANTS OF n POINTS ON THE LINE INTEGRALITY RESULTS
2015/10/14
Consider the projective coordinate ring of the GIT quotient (P1)n//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [HMSV2]we s...
THE RELATIONS AMONG INVARIANTS OF POINTS ON THE PROJECTIVE LINE
RELATIONS AMONG INVARIANTS POINTS ON THE PROJECTIVE LINE
2015/10/14
THE RELATIONS AMONG INVARIANTS OF POINTS ON THE PROJECTIVE LINE.