ShanzhongSUN

• 为促进国内研究天体力学相关课题之数学家、天文学家与物理学家间的交流与合作，藉以提升国内天体力学之研究水平，与台湾清华大学数学系的陈国璋教授和南京紫金山天文台的傅燕宁教授于2019年共同发起了“天体力学数学理论研讨会”。

• 自2017年始，每年为大学一年级的学生作科普报告一次，题目涉及：万有引力定律（2017）、神奇的星环（2018）、集异璧（2019）、数学的统一性–从图谈起（2020）、收敛与发散级数（2021）、指数函数（2022）、连分数（2024）、Physical Mathematics（2025）。

• 讨论班报告

  • 2022/10/19: 王维佳 (清华大学), Modular Regulator and Special Double L-values（In 2006, Manin introduced and studied multiple L-functions of cusp forms but currently not many multiple L-values are well-understood. Beilinson (1986) defined the Eisenstein symbol in the motivic cohomology of the universal elliptic curve and the work of Deninger–Scholl (1989) shows the Petersson inner product of its regulator gives us L-values. In this talk I will present how to relate this modular regulator with double L-values and iterated integrals of Eisenstein series.）
  • 2022/11/30: 束红非（BIMSA），TBA/WKB correspondence and Resurgent Quantum Mechanics （In this talk, we derive a system of thermodynamics Bethe ansatz (TBA) equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These TBA equations provide a solution to the Riemann-Hilbert problem of WKB periods in resurgent Quantum Mechanics. Combined with the exact quantization condition, our TBA equations provide a powerful method to solve the spectral problem. If time allows, we will also mention recent achievements on the higher order ODE.）
  • 2023/03/08: 王智拓（哈尔滨工业大学数学研究院）， Construction Renormalization of the two dimensional Grosse-Wulkenhaar model（The Grosse-Wulkenaar model is a non-integrable matrix model with quartic interaction. It is the first renormalizable model in non-commutative quantum field theory and is closely related to the Kontsevich model for the study of the two dimensional quantum gravity. In this talk I will present some results about the construction of the two-dimensional Grosse-Wulkenhaar model with renormalization group analysis.）
  • 2023/03/28：周贝加（北京大学），Fredholm Theory for Real Pseudoholomorphic Curves in Symplectization （In the symplectization of a contact manifold, people can consider the Symplectic Field Theory (SFT) in all odd dimensions and Embedded Contact Homology (ECH) in dimension 3. Because there is Real Gromov-Witten Theory and Real Seiberg-Witten Theory, it is a natural idea that Real SFT and Real ECH should exist. The first step to construct those theories is to get Fredholm index for moduli space of real pseudoholomorphic curves in symplectization. By this formula of Fredholm index, we can get parallel index inequalities for real pseudoholomorphic curves as in ECH, which is crucial to define Real ECH. I will give and explain the formula of Fredholm index and index inequalities. Other parts of the project of define Real SFT and Real ECH will be mentioned as well.）
  • 2023/09/25：高鸿灏（清华大学），切触拓扑中的刚性性质（勒让德纽结是三维切触空间中的重要几何结构。他们的拉格朗日填充可以用来研究4维辛流形。通过代数不变量，我们可以对勒让德纽结和拉格朗日填充进行分类，即切触拓扑与辛拓扑中的刚性研究。我们将对一些刚性性质进行介绍。）
  • 2023/09/28：王维佳（清华大学），A regularization approach to automorphic forms （In this talk I will explain work in progress with H. Zhang, in which we develop a new regularization technique using Écalle’s transseries. This has led to numerous applications to study automorphic forms. I will talk about some of our results and the key steps in these works.）
  • 2023/10/18：范辉军（北京大学），Progress on the study of Gauged linear Sigma models （Gauged linear sigma model (GLSM) proposed by Witten nearly thirty years ago was used to explain the mirror symmetry phenomena. GLSM relates to many important conjectures, like Landau-Ginzburg A model mirror to Landau-Ginzburg B model, Calabi-Yau model to Landau-Ginzburg model correspondence. GLSM has also intimate relation with GIT and can also be formulated in category theory. This report gives a short survey on the recent progress on this topic.）
  • 2023/11/08：邓嘉龙（清华大学），Positive Scalar Curvature: Existence and Rigidity （The scalar curvature of a Riemannian metric is interesting not only in analysis, geometry, and topology, but also in physics. Enlargeable Length-structures will be introduced and showed that it is a new obstruction to the existence of a Riemannian metric with positive scalar curvature (PSC-metric). Thus, the connected sum of a closed manifold with some of locally CAT(0)-manifolds carry not PSC-metrics. We will also show that almost non-positive curved manifolds carry no PSC-metrics. On the other hand, harmonic maps with condition C will be used to show the rigidity theorem about the scalar curvature.）
  • 2023/11/08：黄永红（新疆大学）Moduli space of Higgs bundles on DM curves （In this talk, I will present the basic constructions about the moduli spaces of Higgs bundles on Deligne-Mumford curves. To conclude, I will explicitly discrible the moduli space of rank 2 Higgs bundles on the pillowcase orbifold curve.）
  • 2023/12/15：顾杰（东南大学）Resurgent structure in topological string (Topological string theory has (spacetime) instanton sectors, which the resurgence theory predicts to be completely controlled by the perturbative free energy via Stokes transformations. Recent results also suggest the Stokes constants are related to BPS/DT invariants. To make this picture concrete, one needs to first solve the instanton amplitudes and then calculate the Stokes constants. We demonstrate that the first problem can be solved exactly and completely through a trans-series extension of the BCOV holomorphic anomaly equations. We also show that valuable information on BPS invariants can be obtained through the calculation of Stokes constants. We will demonstrate our results with the example of the famous quintic manifold.)
  • 2023/12/29：丁祥茂（中国科学院数学与系统科学研究院）Langlands Dualities through Bethe/Gauge Correspondence for 3d Gauge Theories (For non-simple laced Lie algebras, B_N and C_N are Langlands dual to each other in mathematical. In this article, we give two kinds of uniform realizations of Bethe/Gauge correspondence between 3d (or 2d) classical Lie group supersymmetry gauge theory with closed and open XXZ (or XXX) spin chain, the role of the ADE Lie algebras are self-dual, and the non-simple laced Lie algebras BN and CN, their position is exchanged. From Bethe/Gauge correspondence point of view, the two types of the effective superpotentials are Langlands duality to each other. More fantastically, for BN-type Lie algebra, fixed spin site by a boundary through Bethe/Gauge.)
  • 2024/01/05：王百灵（澳大利亚国立大学）Symplectic reductions and quantisations （In this talk, we will first review symplectic reductions, geometric quantisation in terms of index theory and K-theory (K-homology), and the classical [Q, R] =0 theorems. In the second part, we will explore the quantum [Q, R] =0 in symplectic topology with the Q-functor given by QH and QK from the gauge Gromov-Witten theory. This is based on the long ongoing projects with Bohui Chen and Jianxun Hu, and recent work with Bohui Chen and Hailong Her.）
  • 2024/03/15: 赵永恒（国家天文台）LAMOST巡天(LAMOST（Large Sky Area Multi-Object Fiber Spectroscopic Telescope）是中国天文领域的第一个国家大科学装置，是世界上最大的大视场望远镜。LAMOST的主要目标是进行大规模的天体光谱观测，以研究银河系的结构和演化、等天体物理学等领域。巡天范围: 对北半球的大部分天区，包括各种天体目标进行大范围的巡天观测。多目标光谱观测: LAMOST采用了多目标纤维光谱观测技术，使得它能够在一次观测中同时获取近四千个目标的光谱信息，大大提高了观测效率。光谱数据采集和处理: LAMOST通过光纤将目标天体的光线导入光谱仪，获取它们的光谱信息。这些光谱数据包含了目标天体的波长分布和强度，可以用于高精度分析目标源的温度、表面重力、化学成分、运动速度等重要参数。科学研究: LAMOST的巡天数据被广泛用于各种科学研究，包括银河系结构与动力学、恒星和星系的演化等。这些研究对于理解宇宙的结构和演化具有重要意义，极大的推进了相关领域的研究。本报告将对LAMOST软硬件特性、观测数据、科学成果进行深入和全面的分析和概括，为公众和相关研究人员提供丰富而详实的LAMOST信息，促进对LAMOST这一国之重器的了解。)
  • 2024/03/15: 曹子皇（国家天文台）CSST 密集星场天体测量参数解算及其进展 (高精度的自行对于银河系的研究具有极为重要的作用。目前绝大多数银河系的研究都集中在太阳临近和外围区域，而对于保留着银河系早期形成历史和演化轨迹重要证据的核球却缺乏研究。重要原因是由于银河系中心区域恒星密度极高、消光高且不均匀、来自于不同子结构的恒星成分混杂，导致直接获取核球高质量的观测数据十分困难。 由于不受大气的影响，空间观测对于密集星场自行研究优势不言而喻，以HST和Gaia为代表的美国、欧洲空间天文项目已经在相关领域取得了丰硕成果。 可以断定：未来兼顾HST空间高分辨率观测能力和盖亚全天覆盖能力的大口径空间测光巡天数据可以极大地拓展密集星场高精度自行的研究。其中，即将发射的中国2米载人空间站工程巡天空间望远镜（China Space Station Telescope，CSST）就提供了这样一个重要的契机。其光学特性和设计指标，可保证其空间分辨能力与国外同级别空间望远镜相匹敌。对于银心方向，CSST会打破HST数据多限于低消光窗口、样本类型较为单一和Gaia对该区域空间分辨率较低的限制；对于本星系团中的近邻星系/矮星系，CSST会打破HST观测区域不够完备和Gaia观测极限星等较亮的的窘境；从而全面获得这些区域高精度绝对自行信息。 本报告就CSST在密集星场天体测量解算的关键问题进行全面的概括和深入的分析，向学生和相关研究人员展示相关数据处理的前沿观点。)
  • 2024/03/28: 刘会（武汉大学）哈密顿系统与辛动力系统中的闭轨道问题 (闭轨道的存在性、多重性和稳定性的研究是哈密顿系统与辛动力系统的核心内容之一，本报告主要介绍哈密顿能量面上闭特征、切触流形上Reeb闭轨道、Finsler流形上闭测地线等闭轨道问题的研究背景及我们的最新进展。)
  • 2024/04/17：曲华迪（南方科技大学）Action and periodic orbits of area-preserving surface diffeomorphisms（We are interested in the periodic points of area-preserving diffeomorphisms on surfaces. The celebrated Poincare-Birkhoff fixed point theorem and subsequent generalizations revealed the existence and abundance of periodic solutions in Hamiltonian systems, but the good structure of the collection of periodic solutions remains unknown. Converting area-preserving surface diffeomorphisms to Reeb flow via open book decomposition provided a way to relate the dynamics of area-preserving surface diffeomorphisms and the dynamic of Reeb flows of 3-dimensional contact manifolds, and ECH (Embedded Contact Homology) theory proves to be powerful. Though this way ,we want to conduct a quantitative analysis about the distribution of periodic orbit , based on the positive developments by Hutchins in 2016 and Weiler in 2019, our work delves into a more precise examination of the dependency of quantitative results, further generalizing and unifying these two results. Our investigation involves two crucial invariants of surface diffeomorphisms: the mean action and the rotation vector defined on the invariant measure set. We reveals the intrinsic connection between these two invariants, leading to the formulation of a further conjecture that generalize the Poincare-Birkhoff theorem.）
  • 2024/04/17：张建路（中科院数学所）Selection principle of Generalized Hamilton-Jacobi equations（In 1987, Lions firstly proposed the homogenization for Hamilton-Jacobi equations, which revealed the significance of effective Hamiltonian in controlling the large time behavior of solutions. He also pointed out a vanishing discount procedure which is equivalent in obtaining the effective Hamiltonian, yet the convergence of solutions in this procedure was unknown until recently. In a bunch of joint works, we verified this convergence by using dynamical techniques.）
  • 2024/04/19：徐晓濛（北京大学）Explicit evaluation of Stokes matrices via the isomonodromic approach（The Stokes matrices of linear systems and the associated isomonodromy equation play important roles in the study of Frobenius manifolds, stability conditions, representation theory and so on. The isomonodromy equation is a multi-time dependent Hamiltonian system, with the linear system as a Lax representation. Similar to the inverse scattering method, this talk solves the isomonodromy equation in terms of the scattering data, i.e., the Stokes matrices. Equivalently, it gives explicit expression of the Stokes matrices via the boundary values of the isomonodromy equation. As a consequence, many global properties of the solutions of isomonodromy equations can be derived. ）
  • 2024/05/08：廖灵敏（武汉大学）Rational dynamics on the projective line of the field of p-adic numbers（We study rational maps as dynamical systems on the projective line of the field of p-adic numbers. We usually divide the space into two invariant parts: Julia set and Fatou set. For a rational map without critical point, the subsystem on the Julia set is topologically conjugate to some subshift of finite type on an alphabet of finite symbols, i.e., finite states Markov shift, and the subsystem on the Fatou set is described by a decomposition of minimal subsystems. However, if the rational map admits critical points, its dynamical behavior becomes complicated. In general, we prove that for a geometrically finite rational map, i.e., every critical point has finite forward orbit, the dynamics on its Julia set is topologically conjugate to a countable states Markov shift. This is a joint work with Shilei Fan, Hongming Nie and Yuefei Wang.）
  • 2024/06/27: 蒋云峰（堪萨斯大学）A theory of counting surfaces in projective varieties(The theory of enumerative invariants of counting curves (Riemann surfaces) in projective varieties has been an important theory in the last decades.The enumerative invariants were motivated by theoretical physics—string theory and gauge theory, and include Gromov-Witten theory, Donaldson-Thomas theory and more recently Vafa-Witten theory. It is hoped that there may exist a theory of counting algebraic surfaces in projective varieties. A theory of counting surface in a Calabi-Yau 4-fold has been constructed using Donaldson-Thomas theory of 4-folds.In this talk I will try to give evidences of a counting surface theory using stable maps, and explain why it is difficult to construct the counting surface invariants.)
  • 2024/08/19-23: 王明浩（Boston University）短期课程 Feynman Graph Integrals and Configuration Spaces （In this mini-course, I will introduce Feynman graph integrals from topological and holomorphic quantum field theories. For applications, I will sketch a proof of the formality of the configuration space of Euclidean spaces. Finally, I will discuss some conjectures related to the formality problem for the structure sheaf cohomology of configuration spaces. No preliminary knowledge in physics is required for this mini-course. Reference: 1.Pascal Lambrechts, Ismar Volic, Formality of the little N-disks operad, arxiv.0808.0457 2.Maxim Kontsevich, Deformation quantization of Poisson manifolds, arxiv.9709040 3.Minghao Wang, Brian R. Williams, Factorization algebras from topological-holomorphic field theories, arxiv.2407.08667）
  • 2024/09/20: 周正一（中科院数学所）Kahler compactification of C^n and Reeb dynamics (We will present two results in complex geometry: (1) A Kahler compactification of C^n with a smooth divisor complement must be P^n, which confirms a conjecture of Brenton and Morrow (1978) under the Kahler assumption; (2) Any complete asymptotically conical Calabi-Yau metric on C^3 with a smooth link must be flat, confirming a modified version of Tian’s conjecture regarding the recognition of the flat metric among Calabi-Yau metrics in dimension 3. Both proofs rely on relating the minimal discrepancy number of a Fano cone singularity to its Reeb dynamics of the conic contact form. This is a joint work with Chi Li. )
  • 2024/09/25: 宗正宇（清华大学数学系）Remodeling conjecture with descendant(Based on the work of Eynard-Orantin and Marino, the Remodeling Conjecture was proposed in the papers of Bouchard-Klemm-Marino-Pasquetti in 2007 and 2008. The Remodeling Conjecture can be viewed as an all genus open-closed mirror symmetry for toric Calabi-Yau 3-orbifolds. In this talk, I will explain an all genus mirror symmetry for descendant Gwomov-Witten nvariants of toric Calabi-Yau 3- orbifolds. The B-model is given by the Laplace transform of the Chekhov-Eynard-Orantin invariants of the mirror curve. This talk is based on ongoing joint work with Bohan Fang, Melissa Liu, and Song Yu.)
  • 2024/11/20: 乔帅格（北京大学）Lie groupoid structures on regular Donaldson Moduli spaces(In general, moduli spaces in geometry have quotient singularities and the Lie groupoids have advantages in recording these structures in smooth categories. Motivated by this principle, in this talk, we will base on the Donaldson moduli spaces of instantons on 4-manifolds and explain the framework of the construction. This is the joint work with Bohui Chen and Bai-ling Wang.)
  • 2024/12/04: 孟国武（香港科技大学）Tulczyjew’s approach for particles in gauge fields(Tulczyjew’s unified approach to Lagrangian and Hamiltonian descriptions of particle dynamics is quite appealing to geometry-oriented minds. An advantage of this geometric approach is its flexibility in the sense that it can be easily adapted to different settings, especially to systems with singular Lagrangians or subject to constraints. As one more demonstration of its flexibility, in this talk it will be reported that Tulczyjew’s approach also works for particle dynamics in which an electrically charged particle moves in the presence of an external non-abelian gauge field. As a consequence, a nontrivial generalization of the Lagrange equation is obtained.)
  • 2024/12/13: Ryszard Nest（哥本哈根大学） Automorphisms of the Boutet de Monvel algebra (In a remarkable work, Duistermaat and Singer in 1976 studied the algebras of all classical pseudodifferential operators on smooth (boundaryless) manifolds. They gave a description of order preserving algebra isomorphism between the algebras of classical pseudodifferential operators of two manifolds. The subject of this talk is the generalisation of their results to manifolds with boundary. The role of the algebra of pseudodifferential operators that we are interested in is the Boutet de Monvel algebra.The main fact of life about manifold with boundary is that vector fields do not define global flows and the “boundary conditions” are a way of dealing with this problem. The Boutet de Monvel algebra corresponds to the choice of local boundary conditions and is effectively, a non-commutative completion of the manifold. One can think of it as a parametrised version of the classical Toeplitz algebra as a completion of the half-space. What appears in the study of automorphisms are Fourier integraloperators and we will try to explain their appearance - both in boundaryless and boundary case. as it turns out, the non-trivial boundary case introduces both some complications but also some simplifications of the analysis involved, Once this is done, the analysis that we need reduces to a high degree to relatively classical results about automorphisms and homology of the Toeplitz algebra and some basic facts from K-theory. )
  • 2025/04/24: William Mistegard（南丹麦大学）The Automorphism Equivariant Hitchin Index (Let T be the one-dimensional complex torus. We consider the action of an automorphism f of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space M of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index. We prove a formula for it in terms of cohomological pairings of canonical T-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface. The study of the automorphism equivariant Hitchin index is motivated by complex quantum Chern-Simons theory and non-abelian Hodge theory. Further, this index is a generalization of the Witten-Reshetikhin-Turaev quantum invariant of the three-manifold Y obtained as the mapping torus of the automorphism f. This project is based on joint work with J. E. Andersen and G. Ayuso.)
  • 2025/05/27: Alain Albouy（巴黎天文台）The two Levi-Civita regularizations (Levi-Civita published in 1916, and republished in 1920 and 1924, a proof that the flow of the 3-dimensional 3-body problem may be regularized, that is, replaced by a smooth flow which passes the binary collisions without experiencing any kind of singularity. This proof is reproduced by Siegel in his book (1956). But from 1965, all the authors on the reg- ularization of the binary collisions considered that Levi-Civita only did the 2-dimensional case, and that the 3-dimensional case was first proposed in 1964 by Kustaanheimo, who extended in a sophisticated way the 2-dimensional regularization that Levi-Civita used in 1906. This is extremely surprising. What is then the status of Levi-Civita’s result in 1916? He claimed to regularize the flow, without any hypothesis on the value of the energy. If we replace his second regularization by the Kustaanheimo-Stiefel regularization, we cannot regularize the binary collisions with zero energy. If we replace it by Moser’s regularization (1970), which indeed Moser relates to Levi-Civita’s second regularization (see [2] p. 615), we have the same problem. I will propose a very simple improvement of Levi-Civita’s second regularization which confirms his argument. The improved regularization is still simpler than the KS regularization. )
  • 2025/06/17: Campbell Wheeler (法国IHES）Resurgence and hyperbolic knots (I will discuss recent progress on resurgence for quantum invariants of hyperbolic links. I will give proofs of conjectures of Garoufalidis-Gu-Mariño that certain entries of matrices of Stokes automorphisms are given by the 3d-index of Dimofte-Giaotto-Gukov. This is based on work with Fantini and work in progress with Andersen-Fantini-Kontsevich.)
  • 2025/08/19: Urs Frauenfelder教授（德国奥格斯堡大学）GIT quotients and symmetric periodic orbits （This is joint work with Agustin Moreno and Dayung Koh. The restricted three-body problem is invariant under various antisymplectic involutions. These real structures give rise to the notion of symmetric periodic orbit which simultaneously have an open string interpretation as a Hamiltonian chord as well as a closed string interpretation as a periodic orbit. This makes the bifurcation analysis of symmetric periodic orbits very intriguing since under bifurcations two local Floer homologies are invariant, the periodic one as well as the Lagrangian one. In this talk I explain how methods from symmetric space theory can help to extract efficient datas from reduced monodromy matrices of periodic orbits helping to analyse the possible bifurcation patterns.）
  • 2025/10/22: 朱子阳（首都师范大学）Statistical Physics and Kinetic Theory: an introduction (Statistical mechanics can be broadly divided into two parts: equilibrium statistical mechanics and non-equilibrium statistical mechanics. In the case of equilibrium, we define ensembles using Hamiltonian mechanics, while non-equilibrium represents a completely different model known as kinetic theory, which is often used to study the macroscopic evolution of complex systems. I will introduce the physical background of non-equilibrium statistical mechanics and various models, with a particular focus on the Boltzmann equation and the second law of thermodynamics, and present several specific examples.)
  • 2025/10/30: 曹子皇（国家天文台）、单博涛（首都师范大学）天体测量与国家⼤科学⼯程 （本报告将系统阐述天体测量的核心概念、国家大科学工程的战略意义、中国天文领域首个国家大科学工程——郭守敬望远镜（LAMOST）的科学与技术成就，以及中国科学院的定位与使命。报告指出，天体测量（Astrometry）是天文学最基础且最关键的分支，其核心任务是精确测定天体的位置、运动和距离，为天球坐标系统的建立、空间导航以及系外行星探测等奠定了坚实基础。典型代表项目包括欧洲空间局的Gaia卫星、甚长基线干涉测量（VLBI）和中国空间站望远镜（CSST）。在阐释国家大科学工程的内涵时，报告指出，这类工程是国家层面规划建设的重大科研设施，具有高投入、高技术、高产出和高共享等特征，旨在解决前沿科学问题、推动原始创新与关键核心技术突破。国际上具有代表性的案例包括CERN的大型强子对撞机（LHC）、NASA的詹姆斯·韦布空间望远镜（JWST）以及SKA平方公里阵列射电望远镜。报告重点分析了LAMOST作为我国天文领域首个国家大科学工程的重要地位：在科学意义上，它填补了我国在大规模天体光谱观测方面的技术与数据空白；在技术创新上，独创性地采用子午缝结构与可变焦比主镜设计，实现了4000根光纤同时观测的突破；在科学产出上，公开发布了超过2200万条高质量光谱，构建了全球最大的恒星光谱数据库，支撑了银河系结构、恒星化学演化和机器学习星表等多个前沿领域的研究，并培养了大量具有观测与数据处理能力的青年人才，被誉为“中国天文迈向国际主流的起跳板”。在此基础上，报告进一步介绍LAMOST天体测量系统的关键技术突破，包括将整个系统分解为星表场、观测星场、像场和介质场的创新方法，以及通过极坐标与局部导星相机坐标融合实现的高精度建模方案。随后，延伸至中国空间站望远镜（CSST）的天体测量前景，指出其在轨观测不受大气扰动、具备1.1平方度的大视场和优于0.13角秒的空间分辨率，将在密集星场（如银心区、M31、M33及球状星团）联合定标与高精度天测中发挥重要作用。报告将展示基于仿真数据的ePSF、EMPCA以及去混叠（Deblending）算法的最新研究进展，这是报告人在天体测量算法与仿真研究方面的前沿探索。最后，报告重申中国科学院的战略定位：作为国家在科学技术领域的最高学术机构、战略科技力量和综合性科研中心，中国科学院肩负着国家战略科技任务、原始创新和高端人才培养的核心使命。）

Back to Home