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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...
Quantization of bending deformations of polygons in E3,hypergeometric in tegrals and the Gassner representation
bending deformations of polygons E3 hypergeometric in tegrals the Gassner representation
2015/10/14
Quantization of bending deformations of polygons in E3,hypergeometric in tegrals and the Gassner representation.
The A-hypergeometric System Associated with a Monomial Curve
A - hypergeometric system single curve
2014/12/29
The A-hypergeometric System Associated with a Monomial Curve.
The A-hypergeometric system associated with a monomial curve
A - hypergeometric system single curve
2014/12/29
The A-hypergeometric system associated with a monomial curve.
Rational hypergeometric functions
Multivariate hypergeometric function complex curved surface the double circular orbit closures geometric function
2014/12/29
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors project...
The Structure of Bivariate Rational Hypergeometric Functions
Codimension 2 lattice structure configuration rational function F partial derivatives zero complex curved surface
2014/12/24
We describe the structure of all codimension-2 lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all the partial derivatives of which are ...
A new generalization of generalized hypergeometric functions
generalized hypergeometric functions Complex Variables
2012/6/15
In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special ...
Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
Toric Deligne-Mumford stacks GKZ hypergeometric system Algebraic Geometry
2012/5/9
We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the...
Anti de Sitter quantum field theory and a new class of hypergeometric identities
hypergeometric identities High Energy Physics - Theory Anti de Sitter quantum field theory
2011/10/9
Abstract: We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the K\"all\'en-Lehmann representation of products of two Anti-de Sit...
Asymptotic zero distribution of a class of hypergeometric polynomials
Asymptotic zero distribution Hypergeometric polynomials Jacobi polynomials
2011/9/2
Abstract: We prove that the zeros of ${}_2F_1(-n,\frac{n+1}{2};\frac{n+3}{2};z)$ asymptotically approach the section of the lemniscate $\{z: |z(1-z)^2|=4/27; \textrm{Re}(z)>1/3\}$ as $n\rightarrow \in...
Confluent A-hypergeometric functions and rapid decay homology cycles
A-hypergeometric functions decay homology cycles Algebraic Geometry
2011/8/23
Abstract: We study confluent A-hypergeometric functions introduced by Adolphson. In particular, we give their integral representations by using rapid decay homology cycles of Hien.
Hypergeometric summation representations of the Stieltjes constants
Riemann zeta function Stieltjes constants generalized hypergeometric function
2011/7/26
Hypergeometric summation representations of the Stieltjes constants.
Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
Heun's equation generalized hypergeometric function exceptional Jacobi polynomial
2011/7/27
Abstract: We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation ...
Quantum mechanical potentials exactly solvable in terms of higher hypergeometric functions. I: The third-order case
Quantum mechanical higher hypergeometric third-order
2011/7/25
Abstract: We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of ...
Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
Intertwining operators Sklyanin algebra elliptic hypergeometric series
2011/1/18
Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ℓ and −ℓ − 1 are constructed using the technique of intertwin-ing vectors for...