中心开展的网上讨论班信息（2023.1.3-8.3）
2023-02-23 来源：数学科学研究中心活动地点：
活动类型：学术报告
主讲人：
活动时间：2023-01-03 09:00:00--2023-01-03 17:00:00
活动内容：
中心开展的网上讨论班信息（2023.1.3-7.8.3）
浙江大学数学中心：
第 145 周 线下线上讨论班
时间：北京时间8月3日上午9：00～11：00
地点：腾讯会议 （会议号：#腾讯会议：573-5830-8429 无密码）
报告人：周雷
题目：Lie group valued moment maps
摘要：At 1998s, A. Alekseev, A. Malkin, E. Meinrenken proposed the concept of Lie group valued moment maps.
This theory is aimed to prove Witten's intersection pairing formula. So the definition of it has a close relationship
with the moduli space of the flat connections on a Riemann surface. At this time I want to talk about the ideas
behind this definition.
第 145 周 线下线上讨论班
时间：北京时间8月1日上午9：00～11：00
地点：腾讯会议 （会议号：#腾讯会议：573-5830-8429 无密码）
报告人：夏天澄
题目：q-Hamiltonian G-space and heat kernel III
摘要：In this talk, we will try to give a formula of the intersection number of certain characteristic classes
on Φ^-1(e)/G.
第 144 周 线下线上讨论班
时间：北京时间7月27日下午14：00-16：00
地点：腾讯会议 （会议号：#腾讯会议：573-5830-8429 无密码）
报告人：夏天澄
题目：q-Hamiltonian G-space and heat kernel II
摘要：In this talk, we will firstly review the remaining problem in last report，and derive the symplectic
volume formula on q-hamiltonian G-space. After that, we try to give a formula of the intersection number
of certain characteristic classes on Φ^-1(e)/G.
第 144 周 线下线上讨论班
时间：北京时间7月25日上午9：00-11：00
地点：腾讯会议 （会议号：#腾讯会议：573-5830-8429 无密码）
报告人：胡孟戈
题目：Circle bundles, adiabatic limits of η-invariants and Rokhlin congruences
摘要：In this presentation, we first introduce Zhang 's Rokhlin type congruences formula and then
talk about the tools he used, that is the η-forms and the adiabatic limit of η-invariants. As an application,
we give some explicit calculations.
第 143 周 线下线上讨论班
时间：北京时间7月20日上午9：00-11：00
地点：腾讯会议 （会议号：#腾讯会议：573-5830-8429 无密码）
报告人：周雷
题目：An introduction to the moduli space of Higgs bundles
摘要：In this presentation, I will introduce the moduli space of stable Higgs bundle from the perspective of
hyperkahler quotients.
第 143 周 线下线上讨论班
时间：北京时间7月18日上午9：00-11：00
地点：腾讯会议 （会议号：#腾讯会议：573-5830-8429 无密码）
报告人：夏天澄
题目：q-Hamiltonian G-space and heat kernel I
摘要：In this talk, we will firstly review the definitions of q-Hamiltonian G-space. Then we will try to derive a
formula similar to Witten's symplectic volume formula on q-Hamiltonian G-space using the heat kernel.
第 142 周 线下线上讨论班
时间：北京时间7月11日上午9：00-11：00
地点：腾讯会议 （会议号：#腾讯会议：830-475-207 无密码）
报告人：胡孟戈
题目：Modular invariance and Rokhlin congruences
摘要：In this presentation, we first introduce the background of Rokhlin congruences and related results.
Then we talk about modular invariance and give some explicit modular forms that would be used later.
As an application, we prove a higher dimensional "miraculous cancellation" formula. Combining with
the Atiyah-Hirzebruch divisibility, we reprove the Rokhlin congruences.
第 141 周 线下线上讨论班
时间：北京时间7月4日上午9：00-11：00
地点：腾讯会议 （会议号： #腾讯会议：927-580-843 无密码）
报告人：纪正超
题目：流形上两类特征值问题的上下界估计；
摘要：在本次报告中，我们将介绍两类特征值的上下界估计。首先，我们会讨论欧氏空间中Dirichlet特征值问题的
下界估计，针对该问题，我们将分成二维以及高维两种不同的情形分别讨论；其次，我们将研究夹板问题的特征值
在欧氏空间中的下界估计；最后，我们会给出黎曼流形上夹板问题特征值的一些上界估计。
第 140 周 复几何线上讨论班
时间：北京时间6月20日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：184-462-341 无密码）
报告人：周雷
题目：Atiyah–Bott Localization Formula in Equivariant Cohomology
摘要：Atiyah-Bott localization formula states that when a smooth manifold M admits an action of a compact
connected Lie group G then the integral on X localizes at the fixed points. From the perspective of equivariant
cohomology, this is a natural result after we have defined the Thom class and Euler class in equivariant style.
Equivariant cohomology has deep and natural connections to symplectic geometry, since the equivariant
closed symplectic forms are one-to-one correspondence with the moment map, and in this situation the
localization formula could be specialized to Duistermaat-Heckman formula. In this time I want to talk
about this topic.
第 139 周 复几何线上讨论班
时间：北京时间6月13日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：651-713-872 无密码）
报告人： 陈如通
标题： Kähler identities for almost complex manifolds
摘要： First we review classical Kähler identities on Kähler manifolds, including Demailly's generalization
on Hermitian manifolds. Then we talk about these identities on almost Kähler manifolds which uses local
analytic methods. Lastly, we introduce Fernandez and Hosmer's work on general almost complex
manifolds, which formulates the problem in the Clifford bundle of the manifold.
第 138 周 复几何线上讨论班
时间：北京时间6月6日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：598-109-056 无密码）
报告人： 夏天澄
题目：q-Hamiltonian G-space and heat kernel II
摘要：In this talk, we will continue our previous discussion about q-hamiltonian G-space. This time
we will focus on discussing the example of G^2g to explain the relationship between various
measures and forms, then we derive the symplectic volume formula in this case.
第 137 周 复几何线上讨论班
时间：北京时间5月30日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：640-928-282 无密码）
报告人：胡孟戈
Title: Atiyah's index theory method to vector fields
Abstract: In this presentation, we firstly introduce a vanishing theorem for complex vector fields and
then try to give a new systematic proof motivated by Atiyah's method to vector fields. Finally, we talk
about a generalization of this method to the congruences of Euler characteristic and signature.
第 136 周 复几何线上讨论班
时间：北京时间5月23日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：632-202-045 无密码）
报告人：周雷
题目：Weil Algebra and Characteristic Homomorphism
摘要：The characteristic homomorphism, or the Chern-Weil map, could be used to define characteristic classes from the perspective of Weil model, and is crucial for the localization formula. By writting down this homomorphism explicitly, we can learn almost all important concepts about the Weil algebra. In this time I want to introduce this map and the reference book is 'Supersymmetry and Equivariant de Rham Theory'.
第 135 周 复几何线上讨论班
时间：北京时间5月16日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：421-231-381 无密码）
报告人：张良迪
题目：Fully nonlinear parabolic equations on a compact almost Hermitian manifold
摘要：In this talk, we present the uniqueness and long time existence of smooth solutions to a general class of fully nonlinear parabolic partial differential equations on a compact almost Hermitian manifold. Then we show that a suitably normalized solution converges smoothly to a function that is a solution to a class of fully nonlinear elliptic equation up to scaling.
第 134 周 复几何线上讨论班
时间：北京时间5月9日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：556-999-955 无密码）
报告人： 陈如通
题目：Integrals on complex torus
摘要：In this talk, we firstly introduce the integrals of a Kähler form over 2-cycles in a complex torus, then we talk about the relationship between these integrals and projectivity of the torus, lastly, we focus on how these integrals are affected by deformations.
第 133 周 复几何线上讨论班
时间：北京时间5月2日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：691-849-960 无密码）
报告人： 夏天澄
题目：q-Hamiltonian G-space and heat kernel
摘要：In this talk, we will firstly review and compare the definitions of Hamiltonian G-space and q-Hamiltonian G-space. Then we will try to derive a formula similar to Witten's symplectic volume formula on q-Hamiltonian G-space using the heat kernel.
第 132 周 复几何线上讨论班
时间：北京时间4月27日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：378-869-558 无密码）
报告人： 杨普天
Title: Mather theory, KAM and weak KAM theory: a brief introduction
Abstract: Given a smooth non-degenerate $H_0(p)$ and $H_{\epsilon}(x,p) = H_0(p)+\epsilon H_1(x,p)$ the smooth small perturbation of $H_0$, it is well-known that for most of rotation vectors, the invariant KAM tori exist and the dynamics on those tori is conjugated to a rigid rotation. Starting from this aspect, we are going to introduce weak theory and its connection to $N$-body problem.
第 132 周 复几何线上讨论班
时间：北京时间4月25日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：556-715-794 无密码）
报告人： 刘杨杉山
题 目：The uniqueness of convex but non-strictly convex central configurations for the planar Newtonian 5-body problem
摘 要：为了应用Morse临界点理论, 我们使用相对距离坐标系讨论了一种具有梯形凸包的凸但非严格凸的平面5体问题的中心构型, 即其中四个质点位于一个梯形的四个顶点, 第五个质点位于梯形某条平行边上. 我们证明了对于给定凸包上的逆时针循环质量序, 至多存在一个具有此形状的中心构型. 另外, 如果包含三个共线质点的平行边严格短于另一平行边, 那么这个构型一定具有对称性, 即此梯形成为等腰梯形, 而第五个质点位于较短平行边的中点。
第 131 周 复几何线上讨论班
时间：北京时间4月18日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：537-643-532 无密码）
报告人： 胡孟戈
题 目：Adiabatic limit and connections in Finsler geometry II
摘 要：We will first review some results in last presentation. Then we continue to give a key lemma which relate the Bismut-Zhang form and the Cartan tensor. As a result, we prove that the Bott connection of the sphere bundle is exactly the Chern connection. If time permits, we will talk about a Chern-Simons type form on Finsler surface.
第 130 周 复几何线上讨论班
时间：北京时间4月11日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：637-695-828 无密码）
报告人： 胡孟戈
题 目：Adiabatic limit and connections in Finsler geometry
摘 要：In this presentation, we will first review some backgrounds of Finsler geometry. In particular, we would introduce an adapted frame of the sphere bundle of a Finsler manifold which generates a horizontal subbundle and gives a Sasaki metric. Then, we focus on the Chern connection and Bott connection and prove that they coincide on the horizontal subbundle. As a result, the Cartan connection can be realized as the adiabatic limit of the Levi-Civita connection, which gives a global characterization of Cartan connection.
第 129 周 复几何线上讨论班
时间：北京时间4月4日上午9：00-10：00
地点：腾讯会议 （会议号：#腾讯会议：626-135-400 无密码）
报告人： 周雷
题 目：Analytic localization and geometric quantization conjecture
摘 要：Youliang Tian and Weiping Zhang gived an anlytic proof of the geometric quantization conjecture in their joint paper(1998). I think this is a successful case of using Bismut's theory to solve problems in other fields. The geometric quantization conjecture can be understand as 'geometric quantization commutes with symplectic reduction', and I will try to explain these analytic lolization ideas in this presentation.
第 128 周 复几何线上讨论班
时 间: 北京时间3月14日上午9:00-10:00
地 点: 腾讯会议（会议号：829-601-197 无密码）
报告人: 陈如通
题 目：Deformed Dolbeault cohomology classes and VHS
摘 要：In this presentation, we study the theory of variation of Hodge structures (VHS) for a compact complex manifold whose Frölicher spectral sequence degenerates at E_1, using the tools of deformed Dolbeault cohomology classes established by Xia Wei, this work can be seen as a generalization of VHS for ddbar-manifolds also developed by Xia.
第 127 周 复几何线上讨论班
时 间: 北京时间3月7日上午9:00-10:00
地 点: 腾讯会议（会议号：626 307 679 无密码）
报告人: 张梦怡
题 目：Kahler structures for holomorphic submersions
摘 要：Let X, B be compact complex manifolds. In this report we assume that there is a holomorphic submersion \pi: X ->B. We can derive a criterion for X to be a Kahler manifold. This criterion generalizes Blanchard’s criterion for a special class of isotrivial holomorphic submersions. And we can use this criterion to answer a question of Harvey-Lawson in the case of fiber dimension one.
第 126 周 复几何线上讨论班
时 间: 北京时间2月28日上午9:00-10:00
地 点: 腾讯会议（会议号: 211-080-465无密码)
报告人: 刘 凯
题 目：A generalization of Thorpe’s inequality
摘 要：We will talk about a generalization of Thorpe’s inequality. It is an inequality between the Euler characteristic and k-th Pontryagin number of a 4k-dimensional manifold. First we recall some background especially in dimension 4. In this case, the inequality was called Hitchin-Thorpe inequality.
第 125 周 复几何线上讨论班
时 间: 北京时间2月21日上午9:00-10:00
地 点: 腾讯会议（会议号: 170-013-522无密码）
报告人: 毕翔程
题 目：On the Rigidity Theorem for Ancient Solutions of Mean Curvature Flow
摘 要：In this presentation, I will introduce the rigidity of ancient solutions of mean curvature flow in Euclidean space. We will first prove the rigidty theorem under certain low entropy conditions, then we generalize Ecker's local regularity theorem. Finally, we generalize Nakauchi's mean value estimate of solutions of MCF on hypersurface.
第 124 周 复几何线上讨论班
时 间: 北京时间2月14日上午9:00-10:00
地 点: 腾讯会议（会议号: 142-003-920无密码)
报告人: 夏天澄
题 目：Two dimensional gauge theories revisited III
摘 要：In this talk, we will focus on the last part of Witten's paper (Two dimensional gauge theories revisited). We will first introduce the generators of the cohomology classes of the moduli space of flat connections on a 2-dimensional surface. Then the intersection pairings in the case of Non-trivial SO(3)-bundle will be computed as an example. Finally, we will extend the intersection number formula to the general case.
第 123 周 复几何线上讨论班
时 间: 北京时间2月7日上午9:00-10:00
地 点: 腾讯会议（会议号: 953-042-875无密码）
报告人: 胡孟戈
题 目：Witten deformation and analytic localization
摘 要：In this presentation, We talk about deformation of Dirac operators and analytic localization technique. First we give some motivations and backgrounds. Then we prove the Poincare-Hopf index theorem by analytic localization. Finally, we briefly talk about the holomorphic Lefschetz formula and some related topics.
第 122 周 复几何线上讨论班
时 间: 北京时间1月31日上午9:00-10:00
地 点: 腾讯会议（会议号: 631-094-380无密码)
报告人: 周雷
题 目：Novikov inequalities review
摘 要：At this time I want to introduce the Novikov numbers with respect to a de Rham complex twisted by an arbitrary flat bundle. The interests are the applications of the Witten deformation technique in proving a series of Novikov Morse-type inequalities for closed 1-forms. In this topic I will introduce the study of the kernels of the Witten Laplacians on a manifold with a cylindrical end which lead to a version of Novikov inequalities.
第 121 周 复几何线上讨论班
时 间: 北京时间1月17日上午9:00-10:00
地 点: 腾讯会议（会议号: 706 090 158无密码)
报告人: 陈如通
题 目: Deformations of holomorphic line bundles
摘 要: In this presentation, we will use the exponential operator to study the deformations of holomorphic vector bundles, especially holomorphic line bundles, then we introduce the Maurer-Cartan equation and Kodaira-Spencer map for holomorphic line bundles. Last, we will talk about the Kuranishi maps of complex manifolds, holomorphic line bundles and pairs, and the relationships between these three maps.
第 120 周 复几何线上讨论班
时 间: 北京时间1月3日上午9:00-10:00
地 点: 腾讯会议（会议号: 831 074 774无密码)
报告人: 刘 凯
题 目: A Spinorial Quasilocal Mass
摘 要: In this presentation, we first review the history of quasilocl mass. Then we will talk about some recent works of J. Lott. He defined a quasilocal energy of a compact manifold with boundary, relative to a background manifold. The main technique is pulling back dual spinors from the background manifold.
