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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Riemann-Hilbert problem of confluent hypergeometric systems and Seiberg-Witten curves
超几何系统 塞伯格-维滕曲线 黎曼-希尔伯特问题
2023/4/21
This talk first solves explicitly a Riemann-Hilbert problem of confluent hypergeometric systems. It then conjectures and proves a special case that the WKB approximation of the monodromy data of confl...
We describe a geometric–combinatorial algorithm that allows one, using solely the system of weights and roots, to determine the Hesselink strata of the null-cone of a linear representation of a reduct...
Problème de Plateau, équations fuchsiennes et problème de Riemann-Hilbert
Plateau problem polygonal boundary three-dimensional euclidean space
2010/4/6
This dissertation is devoted to the resolution of the Plateau problem in the case of a polygonal boundary in the three-dimensional euclidean space. It relies on a method developped by Ren\'e Garnier a...
判定P_n(Γ)的Hilbert基的一个充要
紧李群 不变多项式芽环 Hilbert基
2009/11/12
设Γ是一作用在R^n上的紧李群，P_n(Γ)是Γ不变的多项式芽构成的环. Hilbert-Weyl定理证明了对于P_n(Γ)总存在一组由Γ不变的齐次多项式芽组成的Hilbert基. 然而，如何从Γ不变的齐次多项式芽中选出一组Hilbert基？如何判定Γ不变的齐次多项式芽的一个有限集就是P_n(Γ)的一组Hilbert基？该文借助于Noether环和不变积分的某些基本性质以及奇点理论的有关定理，证明...
The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann--Hilbert problems
multi-component 2D Toda hierarchy orthogonal polynomials Riemann--Hilbert problems
2010/4/7
We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresp...
HILBERT SPACE OF PROBABILITY DENSITY FUNCTIONS BASED ON AITCHISON GEOMETRY
Bayes' theorem Fourier coefficients Haar basis Aitchison distance Simplex Least squares approximation
2007/12/12
The set of probability functions is a convex subset of $L^1$ and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise wh...
Application of Hilbert's Projective metric on Symmetric Cones
Hilbert's projective metric Symmetric cone
2007/12/11
Let $\Omega$ be a symmetric cone. In this note, we introduce Hilbert's projective metric on $\Omega$ in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation...