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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kazdan-Warner equations on compact Riemann surfaces
紧黎曼曲面 卡兹丹-华纳方程 数学
2023/4/28
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
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...
ENERGY OF TWISTED HARMONIC MAPS OF RIEMANN SURFACES
Riemann surface fundamental group flat bundle harmonic map energy Teichmuller space convex cocompact hyperbolic manifold
2015/12/17
The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function E ρ on Teichm¨uller space TS which is a qualitative invariant of the ...
On Nicolas criterion for the Riemann Hypothesis
Nicolas inequality Euler totient Dedekind function Riemann Hypothesis
2011/2/21
Nicolas criterion for the Riemann Hypothesis is based on an inequality that Euler totient function must satisfy at primorial numbers. A natural approach to derive this inequality would be to prove tha...
Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface
Quillen bundle Geometric Prequantization Non-Abelian Vortices Riemann surface
2011/3/3
In this paper we prequantize the moduli space of non-abelian vortices.We explicitly calculate the symplectic form arising from the L2 metric and we construct a prequantum line bundle whose curvature i...
A physics pathway to the Riemann hypothesis
Riemann hypothesis zeta function,quantum mechanics quantum chaos
2011/2/23
We present a brief review of the spectral approach to the Riemann hypothesis,according to which the imaginary part of the non trivial zeros of the zeta function are the the eigenvalues of the Hamilton...
Riemann hypothesis and Quantum Mechanics
Bost-Connes model Riemann Hypothesis Primorial numbers
2011/2/24
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
The ground state energy of a charged particle on a Riemann surface
ground state energy charged particle Riemann surface
2011/3/3
It is shown that the quantum ground state energy of particle of mass m and elec-tric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E0 =...
Riemann hypothesis and Quantum Mechanics
Bost-Connes model Riemann Hypothesis Primorial numbers
2011/3/4
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
We produce for each natural number n 3 two 1–parameter fam-ilies of Riemann surfaces admitting automorphism groups with two cyclic sub-groups H1 and H2 of orden 2n, that are conjugate in the group o...
We show that for any fixed point P0 on a Riemann surface the distinct realizations of cocycles in H1(,O) correspond to the natural appearances of the standard Heisenberg vertex operator algebra (P0...
Addendum to "Energies of zeros of random sections on Riemann surfaces" [arXiv:0705.2000]. Indiana Univ. Math. J. 57 (2008), no. 4, 1753-1780
Energies of zeros of random sections Riemann surfaces
2010/12/9
The purpose of this note is to resolve an apparent discrepancy between the calculations
in the article [ABS] of Armentano- Beltran-Shub (henceforth ABS) and that in Qi Zhong’s
article [Zh] of the as...
The topology of balls and Gromov hyperbolicity of Riemann surfaces
Topology of balls uniformly separated sets Riemann surfaces Gromov hyperbolicity
2010/12/9
For each k > 0 we find an explicit function fk such that the topology of S inside the ball
BS(p, r) is ‘bounded’ by fk(r) for every complete Riemannian surface (compact or noncompact) S with K W...
Analysis of Riemann Zeta Function Zeros using Pochhammer Polynomial Expansions
Riemann Zeta function Riemann Hypothesis Entire functions Real zeros
2010/12/7
The Riemann Zeta function ζ(s) can be expressed in terms of the entire function ξ(s)which has an integral representation characteristic of a general class of entire functions symmetric
around s = &fr...
Parahoric bundles on a compact Riemann surface
Stable vector bundles parahoric groups parabolic bundles
2010/12/8
Let Y be a smooth projective curve (defined over the ground field C) with an action of a finite group . Let X be the smooth projective curve Y/ and let p : Y → X be the quotient mo...