中心开展的网上讨论班信息(截至10.19)

2021-02-24 来源:数学科学研究中心

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活动时间:2021-03-23 12:23:47--2021-03-23 12:23:47

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中心开展的网上讨论班信息(截至10.19

浙江大学数学中心:



第 63 周 复几何线上讨论班

时   间:  北京时间10月19日上午9:00-10:00

地   点:  腾讯会议(会议号: 904 083 342无密码)

报告人:  刘   凯

题    目:  The Schwarz lemma in Kahler and non-Kahler geometry 

摘    要: In this presentation, we first review the history of the famous Schwarz lemma, then we will talk about K. Broder’ work. He introduced two new curvatures and gave a unified perspective of the various forms of the Schwarz lemma. This leads to novel Chern-Lu, Aubin-Yau, and Chen-Cheng-Look Schwarz lemmas in both the Kahler and non-Kahler category.



第 62 周 复几何线上讨论班
时   间:  北京时间10月5日上午9:00-10:00
地   点:  腾讯会议(会议号:703 093 952无密码)
报告人:  夏天澄
题   目:The Deformation Limits of Moishezon manifolds
摘   要:In this talk, we will review D.Popovici's paper "Adiabatic Limit and Deformations of Complex Structures" , 

which consider the conjecture that the deformation limit of Moishezon manifold is still a Moishezon manifold.



第 61 周 复几何线上讨论班
时   间:  北京时间9月28日上午9:00-10:00
地   点:  腾讯会议(会议号:706 088 400无密码)
报告人:  陈如通
题   目∶VHS for ddbar-manifolds and algebraic approximations
摘   要: We will introduce Xia's work on VHS for ddbar manifolds and use it to prove a theorem about Moishezon deformations of manifolds in Fujiki class C, then we

 give a brief introduction to Lin's work about algebraic approximations of compact Kähler manifolds of 

algebraic codimension 1.




第 60 周 复几何线上讨论班
时   间:  北京时间9月21日上午9:00-10:00
地   点:  腾讯会议(会议号:573 017 176无密码)
报告人:  周雷
题    目:  Brownian Motion on a Riemannian Manifold
摘    要:  Bismut proved both  nondegenerate and degenerate Morse inequality by a probabilistic construction 

of the heat kernel(1986). To figure out the proof, firstly we must learn the Brownian Motion on a Riemannian

 manifold. In this presentation I will talk about Brownian motion, and the stochastic calculus on a Riemannian manifold.


第 59 周 复几何线上讨论班

时   间:  北京时间9月14日上午9:00-10:00

地   点:  腾讯会议(会议号:153 031 304无密码)

报告人:  胡孟戈

题    目:  Getzler rescaling and local index theorem for twisted Dirac operator

摘    要:  In this presentation, we introduce a heat kernel proof of local index theorem  given by Getzler. 

The key step is to rescale not only the space and time but also the Clifford algebra. Then let the rescaling 

parameter tend to zero, we obtain the limit of the rescaled heat kernel is the heat kernel of generalized 

harmonic oscillator, which is well known in physics. If time permits, we would talk about some classical 

index theorem and constructing Mathai-Quillen's Thom form by Getzler rescaling.


第 58 周 复几何线上讨论班

时   间:  北京时间9月7日上午9:00-10:00

地   点:  腾讯会议(会议号: 669 097 571无密码)

报告人:  魏定畅

题    目:  \p-complex and \p-Neumann operator on the Fock space

摘    要:  We will report the following paper concerning the \p operator and \p-Neumann operator on the Fock space,

develop their basic properties and discuss some possible generalizations.


第 57 周 复几何线上讨论班

时   间:  北京时间8月31日上午9:00-10:00

地   点:  腾讯会议(会议号: 383 036 578无密码)

报告人:  刘   凯

题    目:  On the total Betti number of an almost complex manifold.

摘    要: In this presentation, we will talk about J. Hu’ work on the minimal total Betti number of a closed almost complex manifold. The main result is that if the dimension is no less than 8, then the minimal total Betti number is 4. This confirms a conjecture of D. Sullivan except for dimension 6.


第 56 周 复几何线上讨论班

时   间:  北京时间8月24日上午9:00-10:00

地   点:  腾讯会议(会议号: 278 022 079无密码)

报告人:  夏天澄

题    目:  Kodaira-Spencer's maps in differential graded algebra-language

摘    要:  In this topic, we review the deformation theory from the differential graded viewpoint, through the topic we follows the M.Manetti Lectures on deformation of complex manifolds. In this talk, we begin with a brief introduction of dg-vector spaces and dg-algebras, after that, we associate every deformation to its algebraic data, which is a pair of morphisms of sheaves of dg-algebras on X_0. This algebraic data encodes the Kodaira-Spencer map.



第 55 周 复几何线上讨论班

时   间:  北京时间8月17日上午9:00-10:00

地   点:  腾讯会议(会议号: 536 041 852 无密码)

报告人:  陈如通

题    目:  Moishezon deformations of manifolds in Fujiki class C and some examples

摘    要:  In this report, we will talk about the proof of a theorem about deformations of manifolds in Fujiki class C. Then we will give some examples of manifolds in class C which can be deformed to Moishezon manifolds.



第54周 复几何线上讨论班

时   间:  北京时间8月10日上午9:00-10:00

地   点:  腾讯会议(会议号:891 023 032无密码)

报告人:  智艳辉

题    目: Hessian manifold and geometric structures on its tangent bundle 

摘    要:  In this report, we will give the definitions of Hessian manifold and special real manifold. After that we will prove the geometric structures on their tangent bundles are  Kahler manifold and special Kahler manifold respectively.



第53周 复几何线上讨论班

时   间:  北京时间8月3日上午9:00-10:00

地   点:  腾讯会议(会议号:427 008 213无密码)

报告人:  周雷

题    目: Morse complex and its application 

摘    要:  In this topic, we will introduce Pseudo-Gradient field of a Morse function and investigate the integral curves of it to form a complex called “Morse complex”. This complex depends on the numbers of critical points of the Morse function. As an application, we will use the complex to calculate the first Betti number of a smooth  projective variety in CP2 induced by a degree d irreducible polynomial.



第52周 复几何线上讨论班

时   间:  北京时间7月20日上午9:00-10:00

地   点:  腾讯会议(会议号:785 043  428 无密码)

报告人:  胡孟戈

题    目:  Witten's approach to localization and Morse inequality

摘    要:  we will review the celebrated paper of Witten motivated by supersymmetric quantum mechanics which talks about an analytic method to Morse theory. The main idea is to deform the Laplacian by time parameter and Morse function. Then we would see when the time parameter goes infinity, there are finite eigenvalues of deformed Laplacian approach to zero whose eigenfunctions are localized to neighborhood of critical points. Thus we obtain Morse inequality by Hodge theory of deformed Laplacian.


 

第五十一周复几何线上讨论班

时   间:  北京时间7月13日上午9:00-10:00

地   点:  腾讯会议(会议号:340 086  533 无密码)

报告人:  魏定畅

题    目:  Deformations of pairs (I)

摘    要:  We will report the following paper concerning the deformations of a holomorphic pair (X,E), which is an expository of [L.Huang 95].

In the first time we focus on how to derive the DGLA and Maurer-Cartan equation.



第五十周复几何线上讨论班

时间:  北京时间7月6日上午9:00-10:00

地点:腾讯会议(会议号:817 053  805 无密码)

报告人:刘  凯

题目:On the stability of Riemannian manifold with parallel spinors

摘要:In this presentation, we will talk about X. Dai, X. Wang and G. Weis’ works on the stability of Riemannian manifold with parallel spinors. The main result is that Ricci flat metrics which also admit nonzero parallel spinors are stable as the critical points of the total scalar curvature functional. The key step is to find a Bochner type formula.



第四十九周复几何线上讨论班

时间:  北京时间6月29日上午9:00-10:00

地点:腾讯会议(会议号:953 034  874 无密码)

报告人:夏天澄

题目:M.Levine's result about pluri-canonical divisor on Kahler manifolds

摘要:In this report, I will review M.Levine's paper in 1983, which discuss the behavior of pluri-canonical divisor on Kahler manifolds or on manifolds in Fujiki class under the deformation. And as a result, he proved the invarience of m-genus on Kahler manifolds under deformation with some certain requirement.


第四十八周论文讨论班

时间:北京时间6月22日上午9:00-10:00
地点:腾讯会议(会议号: 191 743 812 无密码)
报告人:陈如通
题目:An extended Kodaira-Spencer functional
摘要:In this report, we will talk about the basics of DGLA and generalized deformations of complex structure, then we will talk about an extension of the Kodaira-Spencer functional to Calabi-Yau manifolds of any dimension.

 

第四十七周论文讨论班

时间:北京时间6月15日上午9:00-10:00
地点:腾讯会议(会议号: 717 560 136 无密码)
报告人:纪正超
题目:流形上的特征值与曲率流的若干问题
摘要:本文主要成果包括下述内容:
一、高阶特征值的Polya 猜想及其相关问题
二、 特征值比较定理
三、平均曲率流的柱面估计
四、 Reissner-Nordstrom-anti-desitter流形上的一类逆曲率流

 

第四十六周论文讨论班

时间:北京时间6月8日上午9:00-10:00
地点:腾讯会议(会议号: 404 584 674 无密码)
报告人:张良迪
题目:On finite time singularities of the Ricci flow with bounded scalar curvature
摘要:We focus on two papers, which were written by Enders-Muller-Topping and Hamanaka respectively, on the formation of finite time singularities of the Ricci flow with bounded scalar curvature.

 

第四十五周论文讨论班

时间:2021年6月1日上午9:00-10:00
地点:腾讯会议(会议号:390 404 159 无密码)
报告人:魏定畅
题目:Characteristic classes, Chern-Weil theory and examples.
摘要:I will shortly review the construction of characteristic classes using Chern-Weil method followed by two examples, namely the Chern class and Atiyah class, along with their basic properties. Extension of twisted pluricanonical sections.

 

第四十四周论文讨论班

时间:2021年5月25日上午9:00-10:00
地点:腾讯会议(会议号:819 605 548 无密码)
报告人:刘凯

KAI LIU’S REPORT
Title: A new Bochner Technique and its Applications
Abstract:
The Bochner Technique is a magical tool to address problems involving
topology and curvature. In this talk, we first recall the original Bochner Technique and how it was used. Then we talk about the new Bochner Technique
and its applications in K¨ahler geometry. We obtain some new vanishing and
rigidity theorems due to this technique when appropriate curvature conditions
are imposed. Also, we collected some related problems and their progress for
further research.

第四十三周论文讨论班

时间:2021年5月18日上午9:00-10:00
地点:腾讯会议(会议号:755 297 452 无密码)
报告人:夏天澄
题目:Extension of twisted pluricanonical sections
摘要:In this report, we will continue to focus on "Invariance of plurigenera". During the talk, Siu's paper in 2002 ,"Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type" is reviewed which is an extension of his paper in 1998. Moreover, Siu's method will be compared with Paun's , who simplified Siu's method in 2007.

 

第四十二周论文讨论班

时间:2021年5月11日上午9:00-10:00
地点:腾讯会议(会议号:772 863 888 无密码)
报告人:陈如通
题目:Maurer-Cartan equation and unobstructed deformations
摘要:In this report, we will talk about how to use an inductive  process to solve the Maurer-Cartan equation, including Kodaira-Nirenberg-Spencer's method and Tian-Todorov' work. This is preparatory work for the introduction of Liu-Rao's work on Cartan fumula.

 

 

第四十一周论文讨论班

时间:2021年5月4日上午9:00-10:00
地点:腾讯会议(会议号:989 571 577 无密码)
报告人:纪正超
Title: A  Hessian Quotient Curvature flow in the certain manifold
Abstract:  In this talk, we study the asymptotic behaviors for a  Hessian quotient curvature flow in  a Riemannian manifold. We obtain that under suitable convex conditions for the initial surface, one can get apriori estimates for the solution of the flow therefore to prove the flows will exist for all time and the principal curvatures of the evolving surface converge to a constant $\kappa$ when $t\rightarrow+\infty$.

 

第四十周论文讨论班

时间:2021年4月27日上午9:00-10:00
地点:腾讯会议(会议号:444 374 876 无密码)
报告人:周雷
题目: An overview of Morse Theory written by J.Milnor
摘要: We wil focus on introducing how to use the classical Morse Theorem on the path space of a complete Riemmannian manifold,  which is a main topic of this book, and if the time is enough, we will turn to use these conclusions to prove the Bott Periodicity Theorem for the unitary group.

 

第三十九周论文讨论班

时间:2021年4月20日上午9:00-10:00
地点:腾讯会议(会议号:530 815 655 无密码)
报告人:张良迪
题目:A local curvature estimate for the Ricci flow
摘要:We give a talk about the local boundedness of the Riemannian curvature tensor of solutions to the Ricci flow in terms of its inital value on a given ball and a local uniform bound on the Ricci curvature. Moreover, we discuss some applications.

 

 

第三十八周论文讨论班

时间:2021年4月13日上午9:00-10:00
地点:腾讯会议(会议号:270 991 578 无密码)
报告人:魏定畅
题目:Hopf conjecture, K\"ahler hyperbolic ,non-elliptic, parabolic, and recent works
摘要:In order to solve the Hopf conjecture, the key ingredients had been the vanishing of L^2 cohomology groups since [Gro91] and for this purpose three different yet similar conditions were proposed, both were geometric conditions. In this talk, we will review these three conditions with main proofs in [Gro91], [JZ00] and [CX01]. If time permitted, we will give a quick review of recent works by Yang&Chen in [YC18].

 

 

第三十七周论文讨论班

时间:2021年4月6日上午9:00-10:00
地点:腾讯会议(会议号:492 145 316 无密码)
报告人:刘凯

 KAI LIU’S FIFTH REPORT
Title: Vanishing and estimation theorem for Betti and Hodge numbers
Abstract:
A major theme in differential geometry is the question how curvature conditions restrict the topology of the manifold. The main tool to address this question is the Bochner technique. In this presentation, first we will recall the history of this question then we will talk about Petersen and Winks’ new results on the Vanishing and estimation theorem for Betti numbers on Riemannian manifolds and for Hodge
numbers on K¨ahler manifolds.


 

第三十六周论文讨论班

时间:北京时间3月30日上午9:00-10:00
地点:腾讯会议(会议号:138 663 656 无密码)
报告人:陈如通
题目:deformation and complex structure of projective space
摘要:In this report, we will talk about the infinitesimal and global deformations of complex projective spaces, the conjecture of uniqueness of complex structure of projective space and its relationship with the nonexistence of complex structure of 6-dimensional sphere.

 

第三十五周论文讨论班

时间:北京时间3月23日上午9:00-10:00
地点:腾讯会议(会议号:659 953 573 无密码)
报告人:夏天澄
题目:Invariance of plurigenera
摘要:In this report, we will review Siu's paper "Invariance of plurigenera" in 1998, where plurigenera, also called m-genus P_m(X) ( arbitrary positive integer m) , is defined as the dimension of Γ(X,mK_X). This topic has been popular, especially in the past years there have been some new results. After that, we can briefly discuss the recent results.

 

第三十四周论文讨论班

时间:北京时间3月16日上午9:00-10:00
地点:腾讯会议(会议号: 382 442 458 无密码)
报告人:纪正超
题目:Lower Bounds for Eigenvalues of Laplacian
Operator and the Clamped Plate Problem               
摘要:In this talk, we give some lower bounds for several eigenvalues.Firstly, we investigate the eigenvalues λ i of the Laplace operator and prove a sharp lower bound. Moreover, we extent this estimate of the
eigenvalues to general cases. Secondly, we study the eigenvalues Γ i for the clamped plate problem and deliver a sharp bound for the clamped plate problem for arbitrary dimension.

 

第三十三周论文讨论班

时间:北京时间3月9日上午9:00-10:00
地点:腾讯会议(会议号: 216 905 010 无密码)
报告人:周丽
题目:Overview of Hodge theory 2
摘要:This thesis briefly summarizes the Hodge theory on Kahler manifolds. Using the exterior differential operator to introduce the Laplace operator, and then prove the Hodge decomposition theorem.

 

第三十二周论文讨论班

时间:北京时间3月2日上午9:00-10:00
地点:腾讯会议(会议号: 476 615 346 无密码)
报告人:周丽
题目:Overview of Hodge theory
摘要:This thesis briefly summarizes the Hodge theory on Riemann manifolds and Kahler manifolds.  On the Riemann manifolds, we manily describe the relevant concepts. Using the exterior differential operator to introduce the Laplace operator, and then prove the Hodge decomposition theorem. On kahler manifolds, we mainly illustrate the Hodge decomposition theorems.

 

第三十一周论文讨论班

时间:北京时间2月23日上午9:00-10:00
地点:腾讯会议(会议号: 130 966 461 无密码)
报告人:胡茜茜
题目:Application of stochastic control problem in stock market
摘要:This report introduces the transition from continuous optimal control problems to stochastic control problems and the application of stochastic control problems in the stock market.