已开展的网上讨论班信息(截至11.24)

2020-06-30 来源:数学科学研究中心

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活动时间:2020-06-30 12:37:05--2020-06-30 12:37:05

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已开展的网上讨论班信息(截至11.24

 

浙江大学数学中心:

 

 

第二十五周论文讨论班

时间:北京时间1124日上午9:00-10:00

地点:腾讯会议(会议号:166 351 542 无密码)

报告人:陈如通

题目:Projectivity and deformations of some  fiber spaces

摘要:We will first review some theorems about the projectivity of some fiber spaces, and then we will talk about its applications to algebraic approximations of compact Kahler manifolds with some curvature restrictions.

 

第二十四周论文讨论班

时间:北京时间1110日上午9:00-10:00

地点:腾讯会议(会议号:176 848 839 无密码)

报告人:纪正超

题目:Some improvement for the Weyl type inequalities for the Dirichlet eigenvalue problems.

摘要:In this talk, we will investigate non-zero positive eigenvalues of the Laplacian with

Dirichlet boundary condition in an n-dimentional Euclidean space R^n. First, we introduce the background for the Dirichlet problem. Secondly, we  state the development for the Weyl type estimates for the Dirichlet eigenvalues. Last, we give some improved Weyl type estimates for the Dirichlet problem.

 

第二十三周论文讨论班

 

时间:北京时间11月3日上午9:00-10:00
地点:腾讯会议(会议号:259  880 019 无密码)
报告人:张良迪
题目:Curvature Estimates for Four-Dimensional Gradient Ricci Solitons
摘要:We give a talk about three papers on curvature estimates for 4-dimensional gradient shrinking, steady and expanding Ricci solitons, respectively.

 

 第二十二周论文讨论班

时间:北京时间10月27日上午9:00-10:00
地点:腾讯会议(会议号:631 542 683 无密码)
报告人:魏定畅
题目:Extension of plurianticanonical sections over compact Fano Kahler-Einstein manifolds
摘要:First we will review Zhang's work and then give a new method of extending plurianticanonical sections following Liu&Zhu's work.

 

第二十一周论文讨论班

时间:北京时间1020日上午9:00-10:00

地点:腾讯会议(会议号:508 926 396 无密码)

报告人:刘凯

题目:Vanishing and Rigidity Theorems relating to Lichnerowicz Laplacian

摘要:In this presentation, we will talk about Rovenski, Stepanov and Tsyanoks' results on the kernel of Lichnerowicz Laplacians and its applications on Riemannian manifolds. The main method is the Bochner technique. We did some work in the complex case.

第二十周论文讨论班

时间:北京时间1013日上午9:00-10:00

地点:腾讯会议(会议号:610 208 753 无密码)

报告人:夏天澄

题目:Dan Popovici's main work on Deformation and Hodge theory in these years

摘要:In this talk, we will see the main result about Deformation and Hodge theory from D.Popovici. His work listed here is mainly about three part:

(i)Conjecture: the deformation limits of Moishezon mfd is still Moishezon;

(ii)Demailly’s conjecture on transcendental Morse inequalities for differences of two nef classes;

(iii)Hodge Theory on Higer-page of Frolicher Spectral sequence and its application.

 

第十九周论文讨论班

时间:北京时间106日上午9:00-10:00

地点:腾讯会议(会议号:280 222 285 无密码)

报告人:夏天澄

题目:Dan Popovici's main work on Deformation and Hodge theory in these years

摘要:In this talk, we will see the main result about Deformation and Hodge theory from D.Popovici. His work listed here is mainly about three part:

(i)Conjecture: the deformation limits of Moishezon mfd is still Moishezon;

(ii)Demailly’s conjecture on transcendental Morse inequalities for differences of two nef classes;

(iii)Hodge Theory on Higer-page of Frolicher Spectral sequence and its application.

第十八周论文讨论班

时间:北京时间929日上午9:00-10:00

地点:腾讯会议(会议号:170 241 904 无密码)

报告人:陈如通

题目:Splitting theorems and deformations of compact Kahler manifolds

摘要:We will first review some splitting theorems and structure theorems, then we will talk about the relationship between splitting theorems and deformations of compact Kahler manifolds with some curvature restrictions.

 

 

第十七周论文讨论班

时间:北京时间9月22日上午9:00-10:00
地点:腾讯会议(会议号:357 766 640 无密码)
报告人:纪正超
题目:Estimates for the first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres
摘要:In this talk, we will introduce an intersting result of Chen Daguang and  Cheng Qing-ming. In their paper, an optimal upper bounds for the   first eigenvalue of Jacobi operator was obtained, which only depends on the mean curvature H and the dimension n.

第十六周论文讨论班

时间:北京时间915日上午9:00-10:00

地点:腾讯会议(会议号:976 572 996 无密码)

报告人:张良迪

题目:A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature

摘要:We give a talk about R. Buzano and G. Di Matteo's latest paper on the Ricci flow.

 

 

第十五周论文讨论班

时间:北京时间98日上午9:00-10:00

地点:腾讯会议(会议号:494 574 834 无密码)

报告人:张良迪

题目:A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature

摘要:We give a talk about R. Buzano and G. Di Matteo's latest paper on the Ricci flow.

 

 

第十四周论文讨论班

时间:北京时间91日上午9:00-10:00

地点:腾讯会议(会议号:910 546 043 无密码)

报告人:魏定畅

题目:Lp Hodge decomposition on Riemannian manifolds

摘要:报告C.Scott的文章,在闭Riemannian流形上建立类似于L2 Hodge theoryLp Hodge theory, p>1.

 

第十三周论文讨论班


时间:北京时间8月25日上午9:00-10:00

地点:腾讯会议(会议号:464 710 290 无密码)

报告人:韦康

题目:Generalized complex structures and its deformations on the unit disk

摘要: 1) We introduce some basic notations on the generalized complex geometry. 2) We establish generalized L^2-Hodge theory on the unit disk. 3) We study the deformation of   generalized complex structures on the unit disk. 4) We study the relation between the generalized Beltrami differentials and the conformal map on the unit disk.

 

第十二周论文讨论班

时间:北京时间8月18日上午9:00-10:00

地点:腾讯会议(会议号:789259397无密码)

报告人:刘凯

题目:TheBourguignonLaplacianandHermitianbilinearforms摘要:Inthistalk,wefirrstrecallRovenski,StepanovandTsyanoks'resultsonBourguignonLaplacianandSymmetricbilinearformsonRiemannianmanifolds.Thenwegiveacomplexanalogue.WestudythecomplexBourguignonLaplacianonKahlermanifoldsactingonHermitianbilinearforms(SectionsofT^{*1,0}M\otimesT^{*0,1}M.)WemainlyconsiderthetracelessandHarmonicHermitianbilinearforms.UsingthegeneralizedBochnerTechniqueweprovesomerigidityandvanishingtheorems.WealsostudysimilarLaplaciansactingothertensorbundleslikeT^{*1,0}M\otimesT^{*0,1}M.


第十一周论文讨论班

时间:北京时间8月11日上午9:00-10:00

地点:腾讯会议(会议号:504290471无密码)

报告人:夏天澄

题目:ThesGGClassofCompactComplexManifolds

摘要:IwillgiveapresentationaboutDanPopoviciandLuisUgarte'spaper"ThesGGClassofCompactComplexManifolds",inwhichtheystudythecompactcomplexmanifoldswhoseGauduchonconecoincideswiththe(apriorismaller)stronglyGauduchon(sG)coneandgivenumericalcharacterisationsofsGGmanifolds.TheythenusethefakeHodge-Aepplidecompositiontoprovesemi-continuitypropertiesofthepseudo-effectiveandtheGauduchonconesunderdeformations.

 

第十周论文讨论班

时间:北京时间8月4日上午9:00-10:00

地点:腾讯会议(会议号:701575949无密码)

报告人:陈如通

题目:AlgebraicapproximationsofKählermanifolds

摘要:WewillgiveanintroductiontoBuchdahl'sproofofalgebraicdeformationofcompactKählersurfacewithoutunobstructedassumptionandCaoJunyan'spaperonalgebraicapproximaionsofsomecompactKählermanifolds.

 

第九周论文讨论班

时间:北京时间728日上午9:00-10:00

地点:腾讯会议(会议号:478 135 450 无密码)

报告人:夏炜

题目:On the deformed Bott-Chern cohomology

摘要:In this talk, I will report on my recent work on the deformed Bott-Chern cohomology. Given a compact complex manifold $X$ and a integrable Beltrami differential $\phi\in A^{0,1}(X, T_{X}^{1,0})$, we introduce a double complex structure on $A^{\bullet,\bullet}(X)$ naturally determined by $\phi$ and study its Bott-Chern cohomology.

 

第八周论文讨论班

时间:北京时间721日上午9:00-10:00

地点:腾讯会议(会议号:892 647 314 无密码)

报告人:纪正超

题目:Evolution of hypersurfaces in central force fields

摘要:In this talk, we will syudy a result given by   Schnurer and  Smoczyk. They consider flows of hypersurfaces in R^{n+1} decreasing the energy induced by radially symmetric potentials. These flows are similar to the mean curvature flow but different phenomena occur. They show for a natural class of potentials that hypersurfaces converge smoothly to a uniquely determined sphere if they satisfy a strengthened starshapedness condition at the beginning.

 

 第七周论文讨论班

时间:北京时间7月14日上午9:00-10:00

地点:腾讯会议(会议号:548429144无密码)

报告人:魏定畅

题目:Extensionofd-closedformsandapplications

摘要:Following[LZ],weconsiderextensionofd-closedformsoncompactcomplexmanifoldswhichsatisfycertainmildconditions.Asapplications,wegetasimplerproofofinvarianceofHodgenumbercomparingto[RZ],andanewproofofK\''ahlerstability.

第六周论文讨论班

时间:北京时间77日上午9:00-10:00

地点:腾讯会议(会议号:212 989 785 无密码)

报告人:刘凯

题目:Holomorphic mappings into non-negatively curved manifolds

摘要:In this talk, we first recall Stepanov and Tsyganoks’ results on harmonic mappings into non-negatively curved Riemannian manifolds and holomorphic mappings into non-negatively curved Complex manifolds. Then we generalize their results under a weak curvature condition(the non-negative quadratic orthogonal bisectional curvature, NNQOBC for short). Also, considering the identity mapping of a compact Kähler manifold with two different Ka ̈hler metrics, we obtain a uniqueness theorem for Ricci tensor. At last, we consider the harmonic mapping from P^1 to a Kähler manifold with NNQOBC and obtain a rigidity theorem.

 

第五周论文讨论班

时间:北京时间6.30上午9:00-10:00

地点:腾讯会议(会议号:532 136 222 无密码)

报告人:李逸

题目:The square of Nijenhuis tensor and applications, (Jun Ling, arXiv: 2005.08647)

摘要:报告下Ling Jun 最近关于球面上近复结构和复结构的文章。

 

第四周论文讨论班

时间:北京时间623日上午9:00-10:00

地点:腾讯会议(会议号:370 928 751 无密码)

报告人:张良迪

题目:Harnack estimates for a nonlinear diffusion equation on compact Kähler manifolds

摘要:In this talk, we survey the progress of Harnack estimates on manifolds, and prove some Harnack estimates for a positive solution to the equation $\partial_tu=\Delta u+au+bu^{p+1}$ on a compact Kähler manifold.

 

第三周论文讨论班(第二场)

时间:北京时间618日上午9:00-10:00

地点:腾讯会议(会议号:303 986 232 无密码)

报告人:夏天澄

题目:Little notes on the degeneration of Balanced cone and Gauduchon cone.

摘要:We give some basic notes of  three cohomology group and its common cone (Balanced cone & Gauduchon cone)  on the compact complex manifold . Then we discuss the condition that the Gauduchon cone degenerates but Balanced cone does not , using the ddbar-lemma and the isomorphism map between Bott-Chern cohomology group and Aeppli cohomology group, and give the distance of Bx from degeneration.

 

第三周论文讨论班(第一场)

时间:北京时间616日上午9:00-10:00

地点:腾讯会议(会议号:807 800 809 无密码)

报告人:陈如通

题目:Algebraic deformations of compact Kähler surfaces

摘要:Kodaira has proved that every compact Kähler surface is a deformation of an algebraic surface. Buchdahl's paper Algebraic deformations of compact Kähler surfacesgives a short proof of it under the extra assumption that all infinitesimal deformations are unobstructed. My talk is going to introduce the main theorem of Buchdahl's paper.

 

第二周论文讨论班

 时间:北京时间69日上午9:00-10:00

地点:腾讯会议(会议号:614 381 906 无密码)

报告人:纪正超

题目:Ancient solutions of codimension two surfaces with curvature pinching in R^4

摘要:We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in [28] and we also remove the condition that the second fundamental form is uniformly bounded when t (−,−1).

 

第一周论文讨论班

 时间:北京时间62日上午9:00-10:00

地点:腾讯会议(会议号:903 691 934 无密码)

报告人:张良迪

题目:On gradient shrinking and expanding Kähler-Ricci solitons

摘要:In this talk, we prove a compact gradient shrinking Kähler-Ricci soliton with subharmonic scalar curvature is Kähler-Einstein. Moreover, we show that a complete noncompact gradient shrinking Kähler-Ricci soliton with harmonic scalar curvature and nonnegative fourth order divergence curvature (or Bochner) tensor is rigid. We also prove that a classification theorem for complete noncompact gradient expanding Kähler-Ricci solitons.

 

ICCM:

 

16.

 

Time: November 18   9:00am - 10:00am Beijing Time

ZoomLink:   https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

 

Speaker: Valentino Tosatti  (McGill University)

Title: Smooth asymptotics for collapsing Ricci-flat metrics

 

Abstract: I will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to the pullback of a Kahler class from the base. I will present recent work with Hans-Joachim Hein where we obtain a priori estimates of all orders for the Ricci-flat metrics away from the singular fibers, as a corollary of a complete asymptotic expansion.

 

15.

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ICCM Lectures on Geometry

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Title: Finite ball quotients and algebraicity of the Bergman kernel

 

Speaker:  Prof.  Hang Xu (UC San Diego)

 

Time: 8:30 -9:30am (Friday, 2020-09-25)

 

Abstract:  The Bergman kernel is an important biholomorphic invariant of domains in $\mathbb{C}^n$ and, more generally, of complex analytic spaces.  It is a classical problem to characterize simple “model” domains by properties of their Bergman kernels or Bergman metrics. 

In this talk, we shall discuss a characterization of two dimensional finite ball quotients by algebraicity of their Bergman kernels, and some properties of the Bergman metrics on finite ball quotients. This is a joint work with P. Ebenfelt and M. Xiao.

 

 

14.

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ICCM Lectures on Geometry
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Title: Automorphism groups of smooth hypersurfaces
 
Speaker:  Prof. Xun Yu (Tianjin University)

Time: 10:00 -11:00 (Friday, 2020-09-11)

Abstract: I will discuss automorphism groups of smooth hypersurfaces in the projective space and explain an approach to classify automorphism groups of smooth quintic threefolds and smooth cubic threefolds. This talk is based on my joint works with Professor Keiji Oguiso and Li Wei.

 

13.

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ICCM Lectures on Geometry

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Title: Almost complex Hodge theory

 

Speaker:  Prof. Weiyi Zhang (The Univeristy of Warrick, UK)

 

Time: 16:30 -17:30 (Saturday, 2020-09-05)

 

Abstract: In this talk, I will introduce an effective method to solve the $\bar\partial$-harmonic forms on the Kodaira-Thurston manifold endowed with an almost complex structure and an Hermitian metric. Using the Weil-Brezin transform, we reduce the elliptic PDE system to countably many linear ODE systems. By studying the Stokes phenomenon on linear ODE systems, we reduce the problem of finding $\bar\partial$-harmonic forms to a generalised Gauss circle problem.  We show how this is applied to almost complex Hodge theory. In particular, we answer a question of Kodaira and Spencer in Hirzebruch's 1954 problem list that Hodge numbers can vary with different choices of Hermitian metric. This is a joint work with Tom Holt.

 

 

12.

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ICCM Lectures on Geometry

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Title:  Positivity in hyperkaehler manifolds via RozanskyWitten theory

 

Speaker:  Prof. Chen Jiang  (Shanghai Center for Mathematical Sciences, Fudan University)

Time: 16:00 -17:00 (Friday, 2020-08-28)

Abstract:   For a hyperk\"{a}hler manifold $X$ of dimension $2n$, Huybrechts showed that there are constants $a_0, a_2, \dots, a_{2n}$ such that 

$$\chi(L) =\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q_X(c_1(L))^{i}$$

for any line bundle $L$ on $X$, where $q_X$ is the Beauville--Bogomolov--Fujiki quadratic form of $X$. Here the polynomial $\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q^{i}$ is called the Riemann--Roch polynomial of $X$. In this talk, I will discuss recent progress on the positivity of coefficients of the Riemann--Roch polynomial and also positivity of Todd classes. Such positivity results follows from a Lefschetz-type decomposition of the root of Todd genus via the RozanskyWitten theory.

 

11.

Thefollowingistheinformationofthelectureongeometry:Zoom:ID:18430443981Password:ICCMDetailsareasbelow:ICCMLecturesonGeometry----------------------------------------------------------------------Title:CounterexamplestoFujita'sconjectureinpositivecharacteristicSpeaker:Prof.YiGu(SuzhouUniversity)Time:10am-11am(Friday,2020-08-14)Abstract:Inthistalk,weshallpresentcounterexamplestoFujita’sconjectureinpositivecharacteristic.Moreprecisely,givenanyfieldkofpositivecharacteristicandanyintegern∈N+,weconstructasmoothprojectivesurfaceSoverkalongwithanamplelinebundleLonitsothattheadjointlinebundleKS+nLisnot freeofbasepoints.ThisisajointworkwithLeiZhangandYongmingZhang.


10.

Thefollowingistheinformationofthelectureongeometry:Zoom:ID:18430443981Password:ICCMDetailsareasbelow:ICCMLecturesonGeometry----------------------------------------------------------------------Title:Aneigenvalueestimateforthe$\bar{\partial}$-LaplacianassociatedtoaneflinebundleSpeaker:Prof.JingcaoWu(FudanUniversity)Time:10am-11am(Friday,2020-08-07)Abstract:Theasymptoticestimatefortheorderofthecohomologygroup$H^{p,q}(X,L^k)$isacomplicatedproblemincomplexgeometry.Inthislecture,wewillfollowB.Berndtsson’sideatomakeanapproachontheestimatewhen$L$isnef.Firstwedeveloptheharmonictheoryassociatedwithaneflinebundle.Thenwegiveanestimateofthenumberoftheeigenforms.Inparticular,when eigenvalueequalszero,itwillleadtotheasymptoticestimatefortheorderofthecorrespondingcohomologygroup.


 9.

Thefollowingistheinformationofthelectureongeometry:Zoom:ID:18430443981Password:ICCMDetailsareasbelow:ICCMLecturesonGeometry----------------------------------------------------------------------Title:GenericscarringforminimalhypersurfacesalongstablehypersurfacesSpeaker:ProfessorAntoineSong(UCBerkeley)Time:10am-11am(Friday,2020-07-31)Abstract:MinimalhypersurfacesarenaturalgeometricanaloguesofeigenfunctionsoftheLaplacianandaproblemofinterestisthestudyoftheirspatialdistributionintheambientmanifold.IwilldiscussajointworkwithXinZhou,whereweprovethatinagenericclosedRiemannianmanifoldoflowdimension,any2-sidedstableminimalhypersurfaceisthe"scarringlimit"ofasequenceofminimalhypersurfaceswhoseindexandareadivergetoinfinity.Thisphenomenoncontrastswiththepreviouslyexistinggenericequidistributionresult.

 

8.

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ICCM Lectures on Geometry

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Title:  Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones

 

Speaker:  Professor Song Sun (UC Berkeley)

 

Time: 10am -11am (Thursday, 2020-07-23)

 

Abstract:  The Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connections over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle.  This has been extended by Bando-Siu in 1994 to a class of singular Hermitian-Yang-Mills connections on reflexive sheaves. We study tangent cones of these singular connections in the geometric analytic sense, and show that they can be characterized in terms of new algebro-geometric invariants of reflexive sheaves. Based on joint work with Xuemiao Chen (University of Maryland). 

 

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7.

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ICCM Lectures on Geometry

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Title:  M-theory is time-reversal invariant

 

Speaker:  Dan Freed (University of Texas, Austin)

 

Time: 9:30am -10:30am (Friday, 2020-07-17)

 

Abstract:  In joint work with Mike Hopkins we prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. There are two sources of anomalies: the Rarita-Schwinger field and the cubic form for the C-field.  I will explain the general principles behind these anomalies, since they apply in many problems.  Then I'll turn to the specific computations we did to verify this anomaly cancellation.  They include topologial and geometric methods for computing eta-invariants as well as homotopy-theoretic techniques for computing bordism groups. 

 

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6.Thefollowingistheinformationofthelectureongeometry:Zoom:ID:18430443981Password:ICCMDetailsareasbelow:ICCMLecturesonGeometry----------------------------------------------------------------------Title:OntheOhsawa-TakegoshiextensiontheoremSpeaker:Prof.JunyanCao(UniversiteParis6)Time:3pm-4pm(Friday,2020-07-10)Abstract:Sinceitwasestablished,theOhsawa-Takegoshiextensiontheoremturnedouttobeafundamentaltoolincomplexgeometry.WeestablishanewextensionresultfortwistedcanonicalformsdefinedonahypersurfacewithsimplenormalcrossingsofaprojectivemanifoldwithacontrolonitsL^2norm.ItisajointworkwithMihaiPăun..

 

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5.

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ICCM Lectures on Geometry

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Title: A characterization of non-compact ball quotient

 

Speaker: Prof. Ya Deng (IHES)

Time: 3pm -4pm (Friday, 2020-07-03)

Abstract: In 1988 Simpson extended the Donaldson-Uhlenbeck-Yau theorem to the context of Higgs bundles, and as an application he proved a uniformization theorem which characterizes complex projective manifolds and quasi-projective curves whose universal coverings are complex unit balls. In this talk I will give a characterization for quasi-projective manifolds to be uniformized by complex unit balls, which generalizes the uniformization theorem by Simpson. 

 

4.

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ICCM Lectures on Geometry

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Title: Localization of eta invariant

Speaker: Prof. Bo Liu (East China Normal University)

Time: 10:00 am -11:00 am (Friday, 2020-06-26)

Abstract: The famous Atiyah-Singer index theorem announced in 1963 computed the index of the elliptic operator, which is defined analytically, in a topological way. In 1968, Atiyah and Segal established a localization formula for the equivariant index which computes the equivariant index via the contribution of the fixed point sets of the group action. It is natural to ask if the localization property holds for the more complex spectral invariants, e.g., eta-invariant.

The eta-invariant was introduced in the 1970's as the boundary contribution of index theorem for compact manifolds with boundary. It is formally equal to the number of positive eigenvalues of the Dirac operator minus the number of its negative eigenvalues and has many applications in geometry, topology, number theory and theoretical physics. It is not computable in a local way and not a topological invariant. In this talk, we will establish a version of localization formula for equivariant eta invariants by using differential K-theory, a new research field in this century. This is a joint work with Xiaonan Ma.

 

3.

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ICCM Lectures on Geometry

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Title: On a canonical bundle formula with $\R$-coefficients

Speaker: Zhengyu Hu (Chongqing University of Technology)

Time: 10:00 am -11:00 am (Friday, 2020-06-19)

Abstract: In this talk, I will discuss a canonical bundle formula for a proper surjective morphism 

(not necessarily with connected fibers) with  $\R$-coefficients and its applications. Moreover, I will discuss the inductive property of the moduli divisor.

 

2.

The ICCM lecture on Geometry is rescheduled this week. It is at 10:00 am -11:00 am (Saturday, 2020-06-13). 

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ICCM Lectures on Geometry

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Title: Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Speaker: Wenhao Ou (AMSS)

Time: 10:00 am -11:00 am (Saturday, 2020-06-13)

Abstract: In this talk we will discuss the structure of projective manifold $X$ whose tangent bundle contains a locally free strictly nef subsheaf. We establish that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group $\pi_1(X)$ is virtually abelian, then $X$ is isomorphic to a projective space. This is joint work with Jie Liu (MCM) and Xiaokui Yang (YMSC).

 

1.

ICCM Lectures on Geometry

 

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Title: Complex structures on Einstein four-manifolds of positive scalar curvature

Speaker: Peng Wu (Fudan University)

Time: 10:00 am -11:00 am (Friday, 2020-06-05)

Abstract: In this talk we will discuss the relationship between complex structures and Einstein metrics of positive scalar curvature on four-dimensional Riemannian manifolds. One direction, that is, when a four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian, LeBrun, respectively. We will consider the other direction, that is, when a four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We will show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.

Our method relies on Derdzinski's proof of the Weitzenbock formula for the self-dual Weyl curvature.