南方科技大学
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数学系
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学术会议
English
科研讨论班
1970/01/01-1970/01/01
会议概要
Number Theory Seminar
Algebra & Combinatorics Seminar
Computational & Applied Math Seminar
Dynamical Systems Seminar
Financial Math Seminar
Geometry & Topology Seminar
Graduate Student Colloquium
PDE Seminar
Probability & Statistics Seminar
全部
Parallel methods for simulations of 3D incompressible complex flows
On the structure of finite element spaces and its application
深圳市艾滋病防治概况及面临挑战
Quantum fields as derivatives
From Martingale Optimal Transport to McKean-Vlasov Control Problems
Maximizing/Minimizing the Principal Eigenvalues of Multiphase Anisotropic Conductors: Convexification vs. Homogenization
Torus convolutions in conformal field theories
Stable Stable commutator length in 3-manifolds
Recent developments in quantum invariants in dimension three
Non-constant stationary solutions of Euler-Poisson equations for semiconductors
Erd’’os-Ko-Rado Type Theorems for Permutation Groups
Spectral energy transfer and structure function in two-dimensional turbulence
Deep learning theory: The F-Principle and an optimization framework
Optimal fractional factorial split-plot designs when the whole plot factors are important
Exploring Approaches to Natural Hazard Readiness
Understanding and Accelerating Statistical Sampling via PDEs and Deep Learning
The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary
Critical and near-critical models in statistical physics
Substructures of finite classical polar spaces
Isometric embedding of Riemannian manifolds into Euclidean spaces
Regularity Analysis and Strong Approximations of Stochastic Evolution Equations with Multiplicative Noises
Invariance of plurigenera
Mean-Variance Portfolio Problem with Probability Considered
Existence of non-trivial smooth solution of a diffusion equation with a dynamical boundary condition
Numerical Schemes for a Dendritic Crystal Model
Eigenvalue Problem of Nonlocal Diffusion Operator System
增益扩散薄层的均匀化问题
Optimal Stopping Time in Stock Markets
The Maximal Subgroups of Symplectic Groups
Partial Hyperbolic Dynamics In Dimension Three
随机变分不等式的反射梯度方法及分裂方法分析
Investigation on Chen’s algorithm for computing top eigenpair of tridiagonal matrices
Applying the symmetry groups to study the n body problem
Pricing GLWB in the Extended CIR Framework
An Iteratively Decoupled Algorithm with Unconditional Stability for Biot's Consolidation Model
A Well-Balanced Central-Upwind Scheme for a model of Fluid Flows in a Nozzle with Variable Cross-Section
Analysis and Computation of Decoupled Algorithm for a Poroelasticity Model
Optimization Approaches for the Equilibrium Shape of the Solid-State Dewetting
交换代数与代数几何
Foliation in algebraic geometry
Generalizations of the Springer Theorem
【数学系邀请报告】Continuous Optimization for Directed Acyclic Graph (DAG) Learning
微分几何学简介
【数学系邀请报告】Efficient and accurate structure preserving schemes for dissipative nonlinear systems
【数学系邀请报告】Transition threshold problem for the 3-D Couette flow in a finite channel
Satisficing Credibility for Heterogeneous Risks
【数学系邀请报告】Stabilized Hybrid Mixed Finite Element Method for Poroelasticity
【数学系邀请报告】Robust and efficient preconditioning methods for various Maxwell systems
【数学系邀请报告】Efficient spectral methods for PDEs in complex domains
k-多线性宽范数估计和波方程局部光滑化效应
Applied Algebra短期课程
【教学系列报告】复旦大学高等代数课程建设的经验和体会
【教学系列报告】高等代数教学改革与实践
【教学系列报告】中科大线性代数课程介绍
【教学系列报告】兰州大学《高等代数》课程教学改革与实践
【教学系列报告】“高等代数”课程教学的一些思考
【教学系列报告】线性代数一流课程建设的探索与实践
【教学系列报告】从对代数的认识思考代数课程的教学——兼介绍浙江大学拔尖人才班“代数学”课程建设
【教学系列报告】我讲若当标准形
【数学系邀请报告】Deterministic Methods for Stochastic Dynamical Systems
基于雨课堂的后疫情时代混合式教学
问题趋动与转化技能培养
【教学系列报告】《数值计算方法》课程的一体化教学
The volume of the boundary of a Sobolev extension domain
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
1/2-estimate for $\overline\partial$ Equations on Strictly Pseudoconvex Domain with Rough Coefficients
Weighted estimates of the Bergman projection
High Order Semi-implicit WENO Schemes for All Mach Full Euler System of Gas Dynamics
The local Gan--Gross--Prasad conjecture for real unitary groups
【数学系邀请报告】A low order divergence-free H(div)-conforming finite element method for Stokes flows
Physics-informed neural networks for multiscale hyperbolic models for the spatial spread of infectious diseases
【数学系邀请报告】张量鲁棒主成分分析的非凸低秩lp-正则化模型
【数学系邀请报告】Some recent results on compressible Navier-Stokes equations
【数学系邀请报告】Capillary Gravity Water Waves Linearized at Monotone Shear Flows: Eigenvalues and Inviscid Damping
Sharp convergence for sequences of Schr\"{o}dinger means and related generalizations I: Background and Main Results
Sharp convergence for sequences of Schr\"{o}dinger means and related generalizations II: The main idea of the proof
Singular integrals associated with Zygmund dilations
G-equivariant Szeg˝o kernel asymptotics on CR manifolds
体积指数增长的非紧流形上的全局分析
A two term Kuznecov sum formula
Oscillatory integral operators satisfying the Carleson-Sjolin and straight conditions
Global Integrability of the Reciprocal of the Jocobian and the (INV) Condition
Dispersive estimates for the Schrodinger equation with finite rank perturbations
On the number of Pollicott-Ruelle resonances for open hyperbolic systems and Axiom A flows
Uniform estimates for the Hilbert transform along certain variable curves
Wellposedness and scattering for defocusing energy subcritical nonlinear wave equation
（2+1）维退化振荡积分算子的最佳衰减
沿变曲线极大函数与Hilbert变换的有界性
The Garnett-Jones Theorem on BMO space associated with operators
Hyperbolic graphs and discrete potential theory on compact doubling spaces
The initial boundedness of multilinear Hormander multipliers
Chebyshev’s bias and related topics
Around self-similar solutions of the modified Korteweg de Vries equation
Global stability of Kaluza-Klein spacetimes
【数学文化节科普报告】柯西的成就从何而来
Some recent results on PDEs with potentials and the stability of solitons and kinks
Global smooth solutions to 4-D quasilinear wave equations with a class of large initial data
Applying exoflops to Calabi-Yau varieties
Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation
Asymptotic preserving schemes for some stochastic multiscale systems
Multi-period peer-to-peer risk sharing
Risk Functionals with Convex Level Sets
Fixed angle inverse scattering for sound speeds close to constant
Progress on the mixed truncation
Modelling Shallow Flows with a New Set of Hierarchical Equation
Stability Analysis of Several Moment Closure Systems for Shallow Water and Rarefied Flows
The log-local correspondence in Gromov-Witten Theory
Preference Robust Distortion Risk Measure
Automorphic products of singular weight
Stochastic Symplectic Methods of Stochastic Hamiltonian Systems
浅谈数学严谨性-法国数学家柯西
Geometry from categorical enumerative invariants
The restricted projection problems: decouplings, high-low method
Mixing flow and advection-diffusion-reaction equations
Strategic Loss Reporting
Existence and stability of standing waves to Schrödinger-Poisson equations with harmonic potential
On some recent advances in adapted topologies
Non-abelian Hodge theory and the P=W conjecture
从混沌到有序--Ramsey理论简介
Normal numbers with given limit of multiple ergodic averages
Soliton gas in integrable models
寻找最优
Some recent progress about the Erdős similarity problem
体积指数增长的非紧流形上的全局分析
Abstract
体积指数增长的非紧流形，例如 Anti de Sitter 空间和双曲流形，广泛地出现于广义相对论、AdS/CFT 对偶、散射理论等数学物理理论中。这类流形上的全局分析可以用于研究黑洞中波的传播、共形不变量、几何散射及其反问题。
一方面，无穷远附近的体积指数增长条件保证了实分析中方块的覆盖引理不成立，进而使得 Calderón-Zygmund 理论无法推广到此类流形上。这给谱乘子的有界性问题带来了不可克服的困难。
另一方面，体积的指数增长带来了拉普拉斯算子预解式和谱测度在无穷远的指数衰减性，进而赋予了数学物理方程基本解的指数衰减性，增强了其全局积分估计。这一现象与具有有限中心的半单李群上的 Kunze-Stein 现象紧密相关。