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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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：可压缩Navier-Stokes方程Riemann解的稳定性
可压缩 Navier-Stokes方程 Riemann解 稳定性
2023/5/6
可压缩Navier-Stokes方程描述可压缩粘性流体运动的力学规律，是流体力学中的基本方程。如果忽略粘性效应，可压缩Navier-Stokes方程即为无粘的可压缩Euler方程。可压缩Euler方程描述理想流体的运动，是典型的双曲守恒律方程组，其主要特点是：无论初值多么光滑和多么小，解都可能会爆破，形成间断（激波）。如果考虑可压缩Euler方程的Riemann问题，其解具有三种基本波：激波、稀疏...
合肥工业大学数学学院在Riemann猜想的研究上取得新进展（图）
合肥工业大学数学学院 Riemann 新进展 函数
2020/5/16
近日，合肥工业大学数学学院代数与编码课题组吴小胜副研究员，成功处理了Dirichlet L函数的一类修正二次均值，作为应用证明了每个Dirichlet L函数都有超过41.72%的非平凡零点的实部为1/2。因为Riemann zeta函数是一个特殊的Dirichlet L函数，该研究成果同时得到了Riemann zeta函数有超过41.72%的非平凡零点满足Riemann猜想，这个比例是目前国际上...
中国矿业大学数学学院硕士研究生在Riemann-Hilbert方法与可积系统问题方面取得进展（图）
中国矿业大学数学学院 硕士研究生 Riemann-Hilbert方法 可积系统问题
2019/12/10
近日，我校数学学院硕士研究生彭卫琪与导师田守富特聘研究员等在数学物理学领域的著名期刊 Journal of Geometry and Physics上发表题为“Riemann-Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations”的论文。
The "Riemann-Hilbert correspondences" Winter School and Workshop
Riemann-Hilbert correspondences Winter School Workshop
2017/12/20
Recent groundbreaking developments in the theory of irregular holonomic D-modules have brought to light new relationships among D-module theory and other subjects such as Non Commutative Hodge theory,...
The Forgotten Tradition.How the Logical Empiricists missed the Philosophical Significance of the work of Riemann,Christoffel and Ricci
Logical Empiricism Absolute Differential Calculus General Relativity Hans Reichenbach
2016/5/30
The paper attempts to show how the Logical Empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as...
Torsion Limits and Riemann-Roch Systems for Function Fields and Applications
Algebraic curves Jacobian torsion limit
2016/1/23
The Ihara limit (or constant) A(q) has been a central problem of study in the asymptotic theory of global function fields (or equivalently, algebraic curves over finite fields). It addresses global ...
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 ...
Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
2015/12/17
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
GLUING FORMULAS FOR DETERMINANTS OF DOLBEAULT LAPLACIANS ON RIEMANN SURFACES
Determinants of Laplace operators Riemann surfaces bosonization formulas
2015/12/17
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary...
HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES
HIGGS BUNDLES LOCAL SYSTEMS RIEMANN SURFACES
2015/12/17
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
2015/9/29
Goldman gratefully acknowledges partial support by NSF grants
DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research
Award from the General Research Board of the University of
Maryland in Fa...
The energy of harmonic sections of flat bundles of
nonpositively curved (NPC) length spaces over a Riemann surface
S is a function Eρ on Teichm¨uller space TS which is a qualitative
invariant...