ZOOM ID：952 802 9961
Password：314159
15.
Time:14:00-15:30,Thursday, March 28
Speaker:Haozhao Li, USTC
Title:On Ilmanen's multiplicity-one conjecture for mean curvature flow
Abstract:In this talk, we show that if the mean curvature of a closed smooth embedded mean curvature flow in is of type-I, then the rescaled flow at the first finite singular time converges smoothly to a self-shrinker flow with multiplicity one. This result confirms Ilmanen's multiplicity-one conjecture under the assumption that the mean curvature is of type-I. As a corollary, we show that the mean curvature at the first singular time of a closed smooth embedded mean curvature flow in is at least of type-I. This is joint work with Bing Wang.
Tencent Meeting:760 6725 7412
Passcode:678332
16.
Time:9:00-10:30, Monday, April 1
Speaker:Jingwen Chen, UPenn
Title:Mean curvature flow with multiplicity 2 convergence
Abstract:Mean curvature flow (MCF) has been widely studied in recent decades, and higher multiplicity convergence is an important topic in the study of MCF. In this talk, we present two examples of immortal MCF in $R^3$ and $S^n \times [-1,1]$, which converge to a plane and a sphere $S^n$ with multiplicity 2, respectively. Additionally, we will compare our example with some recent developments on the multiplicity one conjecture and the min-max theory. This is based on joint work with Ao Sun.
ZOOM ID：952 802 9961
Password：314159
17.
Time:9:00-10:30,Monday, April 8
Speaker:Man-Chun Lee, CUHK
Title:Gap theorem on manifold with pinched integral curvature bound
Abstract:In Kahler geometry, Ni proved a optimal gap theorem on Kahler manifold with nonnegative bisectional curvature. In this talk, we will discuss some Riemannian analogy under nonnegative curvature and pinched integral curvature bound. This is based on joint work with Chan.
Tencent Meeting:760 6725 7412
Passcode:678332
18.
Time:14:00-15:00, Tuesday, April 9
Venue:E4-201
Speaker:Shihang He, Peking University
Title:Twisted S^1 stability and positive scalar curvature obstruction on fiber bundles
Abstract:In 2006, Rosenberg made the S^1 stability conjecture, which states that for a compact manifold, the property of admitting no positive scalar curvature (PSC) metric is always preserved when multiplying S^1. In this talk, we will first review classical results and recent developments about PSC. Then we will investigate a twisted version of the above S^1 stability conjecture, as well as more generalized problem of the interaction between PSC obstruction on fiber and the total space of a fiber bundle.
19.
Time:15:30-16:30, Tuesday, April 9
Venue:E4-201
Speaker:Haobin Yu, Hangzhou Normal University
Title:Isoperimetry for asymptotically flat 3-manifolds with positive ADM mass
Abstract:In this talk, we will discuss the isoperimetry for asymptotically flat 3-manifolds with positive mass in large scale. We will show that for such manifolds each leaf of the canonical foliation is the unique isoperimetric surface for the volume it encloses. Our proof is based on "fill-in" argument and sharp isoperimetric inequality on asymptotically flat 3-manifold with nonnegative scalar curvature.
20.
Time:15:30-16:30, Thursday, April 11
Venue:E4-201
Speaker:Mingyang Li, University of California，Berkeley
Title:Classification results for Hermitian non-Kahler gravitational instantons
Abstract:We will discuss some classification results for Hermitian non-Kähler gravitational instantons. There are three main results: (1) Non-existence of certain Hermitian non-Kähler ALE gravitational instantons. (2) Complete classification for Hermitian non-Kähler ALF/AF gravitational instantons. (3) Non-existence of Hermitian non-Kähler gravitational instantons under suitable curvature decay condition, when there is more collapsing at infinity (ALG, ALH, etc.). These are achieved by a thorough analysis of the collapsing geometry at infinity and compactifications.
21.
Time:9:00-10:30,Monday, April 15
Speaker:Jinmin Wang, Texas A&M University
Title:Scalar curvature rigidity and Llraull's theorem
Abstract:Llraull's theorem yields that one cannot increase the scalar curvature and the metric of the standard sphere simultaneously. Gromov conjectures this scalar curvature rigidity for incomplete metrics on spheres with two antipital points removed, and more generally warped product metrics. In this talk, I will present our proof of Gromov's conjecture under an extra condition using Dirac operator method, and a counterexample to Gromov's original statement. I will also give a brief introduction to the mu-bubble approach to this problem in dimension four. The talk is based on joint works with Simone Cecchini, Zhizhang Xie, and Bo Zhu.
Tencent Meeting:760 6725 7412
Passcode:678332
22.
Time:14:00-15:00, Friday, April 19
Venue:E4-201
Speaker:Yalong Shi, Nanjing University
Title:Compactness of cscK metrics near the canonical class
Abstract:We shall prove that the set of csck metrics on minimal models constructed by Jian-Shi-Song is precompact with respect to the Gromov-Hausdorff topology. This is joint work with B. Guo, W. Jian and J. Song.
23.
Time:9:00-10:30,Monday, April 22
Host:Jintian Zhu, ITS
Speaker:Yukai Sun, Peking University
Title:Positive mass theorem for asymptotically flat manifolds with isolated conical singularities
Abstract:The well known Positive Mass Theorem states that for an asymptotically flat smooth manifold, if the scalar curvature is nonnegative, then the mass is also non negative. In this talk, we will discuss the Positive Mass Theorem for an asymptotically flat manifold with finitely isolated conical singularities.
Tencent Meeting:760 6725 7412
Passcode:678332
24.
Time:14:00-15:00, Thursday, April 25
Venue:E4-201
Host:Tongrui Wang, ITS
Speaker:Zijun Wang, Shanghai Jiao Tong University
Title:Regularity for some geometric variational elliptic systems
Abstract:In this talk, we discuss the regularity issues of elliptic variational systems defined on manifolds. It places special emphasis on two aspects: the free boundary regularity of weakly H-surfaces into Riemannian manifolds and the interior regularity of weakly H-surfaces into static Lorentzian manifolds. These works are joint with Professor Miaomiao Zhu.
25.
Time:15:30-16:30, Thursday, April 25
Venue:E4-201
Host:Tongrui Wang, ITS
Speaker:Rui Gao, Shanghai Jiao Tong University
Title:Recent results on bubbling analysis for approximate Harmonic maps and H-surfaces
Abstract:Compactness type results are crucial in the exploration of variational problems in both geometry and physics, as they provide a thorough understanding of the solutions’ behavior and the spaces they inhabit. A captivating example of this is the examination of the asymptotic behavior for sequences of approximate harmonic maps. This extends to a more general context, that is, for approximate surfaces with prescribed mean curvature, which are also called H-surfaces for simplicity. In this talk, we will discuss some recent progresses on the asymptotic and qualitative behavior of these entities.
26.
Time:10:00-12:00, Friday, April 26
Venue:E4-201
Host:Xin Fu, ITS
Speaker:Ma Biao, BICMR
Title:On a fully nonlinear elliptic equation with differential forms
Abstract:We introduce a fully nonlinear PDE on Kahler manifolds with a differential form \Lambda. Such PDE unifies several important equations in complex geometry including Monge-Ampère equation, J-equation, and the deformed Hermitian Yang-Mills (dHYM) equation. Based on G.Chen's breakthrough on J-equation and dHYM equation, we prove analytical and algebraic criterions for the solvability of the equation, assuming certain positivity conditions on \Lambda. As an application of our results, we prove the conjecture of Collins-Jacob-Yau for the dHYM equation with small global phase. It is a joint work with Professor Hao Fang.
27.
Time:11:00-12:00, Friday, April 26
Venue:E4-201
Host:Tongrui Wang, ITS
Speaker:Mingxiang Li, Nanjing University
Title:On the positivity of the Q-curvatures of the conformal metrics
Abstract:In this talk, we will consider a conformal metric $g=u^{\frac{4}{n-2m}}|dx|^2$ on $\mathbb{R}^n$ with $n\geq 2m+1$. We show that if the higher order Q-curvature $Q^{(2m)}_g$ is positive with slow decay near infinity, the lower order Q-curvature $Q^{(2)}_g$ and $Q^{(4)}_g$ are both positive if $m$ is at least two. This talk is based on a joint work with Xingwang Xu.
28.
Time:9:00-10:30, Monday, April 29
Host:Jintian Zhu, ITS
Speaker:Jingbo Wan, Columbia University
Title:Rigidity of Area Non-Increasing Maps
Abstract:In this talk, we discuss the approach of Mean Curvature Flow to demonstrate that area non-increasing maps between certain positively curved closed manifolds are rigid. Specifically, this implies that an area non-increasing self-map of $CP^n$, $n \geq 2$, is either homotopically trivial or is an isometry, answering a question by Tsai-Tsui-Wang. Moreover, by coupling the Mean Curvature Flow for the graph of a map with Ricci Flows for the domain and the target, we can also study the rigidity of area non-increasing maps from closed manifolds with positive 1-isotropic curvature (PIC1) to closed Einstein manifolds, where Prof. Brendle’s PIC1 Sphere Theorem is applied. The key to studying the rigidity of area non-increasing maps under various curvature conditions lies in the application of the Strong Maximum Principle along the MCF/MCF-RF. We will focus our attention on one particular case to illustrate the SMP argument. This is a joint work with Professor Man-Chun Lee and Professor Luen-Fai Tam from CUHK.
ZOOM ID：952 802 9961
Password：314159
29.
Time:15:30-17:00, Thursday, May 9
Venue:E4-201
Host:Xin Fu, ITS
Speaker:Junsheng Zhang，University of California, Berkeley
Title:No semistability at infinity for Calabi-Yau metrics asymptotic to cones
Abstract:We proved a "no semistability at infinity" result for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in Donaldson-Sun's 2-step degeneration theory. As a consequence, we establish a polynomial convergence rate result and a classification result for complete Calabi-Yau manifolds with Euclidean volume growth and quadratic curvature decay. This is based on joint work with Song Sun.
30.
Time:9:00-10:30,Monday, May 13
Host:Jintian Zhu, ITS
Speaker:Yi Lai, Stanford University
Title:Riemannian and Kahler flying wing steady Ricci solitons
Abstract:Steady Ricci solitons are fundamental objects inthe study of Ricci flow, as they are self-similar solutions and often arise assingularity models. Classical examples of steady solitons are the most symmetric ones, such as the 2D cigar soliton, the O(n)-invariant Bryant solitons, and Cao’s U(n)-invariant Kahler steady solitons. Recently we constructed a family of flying wing steady solitons in any real dimension n\geq 3, which confirmed a conjecture by Hamilton in n=3. In dimension 3, we showed allsteady gradient solitons are O(2)-symmetric. In the Kahler case, we also construct a family of Kahler flying wing steady gradient solitons with positive curvature for any complex dimension n\geq 2, which answers a conjecture by H.-D.Cao in the negative. This is partly collaborated with Pak-Yeung Chan and Ronan Conlon.
ZOOM ID：952 802 9961
Password：314159
31.
Time:15:00-16:30,Saturday, May 18
Venue:E4-233
Host:Jintian Zhu, ITS
Speaker:Jie Zhou, Capital Normal University
Title:Optimal rigidity estimates of varifolds almost minimizing the Willmore energy
Abstract:In this presentation, we talk about the stability of the Willmore functional. For an integral 2-varifold $V=\underline{v}(\Sigma,\theta)$ in $R^n$ with square integrable generalized mean curvature andfinite mass. If its Willmore energy is smaller thant $4\pi(1+\delta^2)$ and the mass is normalized to be $4\pi$, we show that $\Sigma$ is $W^{2,2}$ and bi-Lipschitz close to the round sphere in a quantitative way when $\delta<\delta_0\ll1$. For $n=3$, we show the sharp constant is $\delta_0^2=2\pi$. This is a joint work with Dr. Yuchen Bi.
32.
Time:9:00-10:30,Monday, May 20
Host:Jintian Zhu, ITS
Speaker:Shihang He, Peking University
Title:Relative aspherical conjecture and higher codimensional obstruction to positive scalar curvature
Abstract:Motivated by the solution of the aspherical conjecture up to dimension 5 by Chodosh-Li and Gromov, we introduce a relative version of the aspherical conjecture. More precisely, we seek to explore the impact of a codimension k submanifold X on the existence of PSC (Positive Scalar Curvature) of the ambient space Y, under the relative aspherical condition that \pi_i(Y,X)=0, 2\leq I\leq k. The formulation of the conjecture genralizes the aspherical conjecture and Rosenberg S^1 stability conjecture into a single framework, and is closely related to codim 2 obstruction results by Hanke-Pape-Schick and Cecchini-Rade-Zeidler. In codim 3 and 4, we show how 3-manifold obstructs the existence of PSC under our relative aspherical condition, the proof of which relies on a newly introduced geometric quantity called the spherical width. These results could be regarded as a relative version extension of the aspherical conjecture up to dim 5.
Tencent Meeting:760 6725 7412
Passcode:678332
33.
Time:14:00-15:00,Tuesday, May 21
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Linsheng Wang, Nanjing University
Title:Optimal destablizations of Fano varieties
Abstract:Delta invariant, which is also called of stability threshold, is an essential invariant in the study of K-stability of Fano varieties. In this talk, I will introduce Liu-Xu-Zhuang theory about the existence of divisorial valuations mininizing delta invariants.
34.
Time:14:00-15:00,Wednesday, May 22
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Yuto Yamamoto, RIKEN iTHEMS
Title:The Gross--Siebert program and non-archimedean SYZ fibrations
Abstract:For a maximally degenerate Calabi--Yau variety, the Berkovich retraction associated with a (good) minimal dlt model is regarded as an SYZ fibration in non-archimedean geometry. In general, the integral affine structure induced on the base space of the fibration differs from the one defined for the dual intersection complex of a toric degeneration in the Gross--Siebert program. In this talk, using tropical geometry, we construct non-archimedean SYZ fibrations whose bases are integral affine manifolds appearing in the Gross--Siebert program for Calabi--Yau complete intersections of Batyrev--Borisov.
35.
Time:10:00-11:00,Thursday, May 23
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Zexuan Ouyang, Peking University
Title:Constructing Special Lagrangian Fibrations via Higgs Bundles and Affine Structures
Abstract:In this talk, we explore the construction of special Lagrangian (SLag) fibrations using Higgs bundles, based on the work of Heller, Ouyang, and Pedit. We will discuss how solutions to Hitchin's equations provide an affine structure on the base space, derived from a hyperbolic affine sphere and a parabolic Higgs bundle. This affine structure is crucial for forming SLag fibrations, key to understanding mirror symmetry and Calabi-Yau manifolds.
36.
Time:14:00-15:00,Friday, May 24
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Yu Li, University of Science and Technology of China
Title:Uniqueness of the Tangent Flow of the Ricci Flow
Abstract:We prove the uniqueness of the tangent flow of the Ricci flow when one tangent flow is a generalized cylinder. The proof is based on a quantitative characterization of the rigidity of compact Ricci shrinkers, a rigidity inequality of mixed orders on generalized cylinders, and the method of contraction and extension developed by Colding and Minicozzi. This is joint work with Wenjia Zhang.
37.
Time:14:00-15:00, Tuesday, May 28
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Yueqing Feng, UC Berkeley
Title:A gluing construction of constant scalar curvature Kähler metrics of Poincaré type
Abstract:In this talk, we construct new examples of constant scalar curvature Kähler(cscK) metrics of Poincaré type from existing cscK ones. The construction is obtained via gluing a cscK metric on a compact Kähler manifold to a complete scalar-flat Kähler metric of Poincaré type on the complex space removing the origin. Assuming the compact Kähler manifold has no non-trivial holomorphic vector field, we prove the existence of cscK metrics of Poincaré type on this compact manifold removing finitely many points.
38.
Time:14:00-15:00,Wednesday, May 29
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Ziyi Zhao, Peking University
Title:Steady Ricci soliton with nonnegative curvature away from a compact set
Abstract:In this talk, we analysis the blow-down solutions for $n$-dimensional $(n\ge 4)$ noncompact $\kappa$-noncollapsed steady gradient Ricci solitons $(M, g)$ with $\rm{Rm}\geq 0$ and ${\rm Ric}>0$ away from a compact set of $M$. As one of main results, we classified the $(n-1)$-dimensional compact split limit ancient Ricci flows. Consequently, we prove that $(M,g)$ with $\rm{Rm}\geq 0$ must be isometric to the Bryant Ricci soliton up to scaling, if there exists a sequence of normally rescaled Ricci flows of $(M,g)$, which converges subsequently to a family of shrinking quotient cylinders. The later improves a previous result of Brendle. This is a joint work with Xiaohua Zhu.
39.
Time:14:00-15:00,Friday, May 31
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Minghao Miao, Nanjing University
Title:Optimal Degenerations of K-unstable Fano Threefolds
Abstract:In this talk, we will propose a question of how to explicitly determine the optimal degenerations of the K-unstable Fano manifolds as predicted by the Hamilton-Tian conjecture. We answer this question for a family of K-unstable Fano threefolds (No 2.23 in Mori-Mukai's list), which has discrete automorphism groups and the normalized Kahler-Ricci flow develops Type II singularity. Our approach is based on a new method to check weighted K-stability, which generalizes Abban-Zhuang's theory to give an estimate of the weighted delta invariant by dimension induction. Some speculative relations between the delta invariant and the H invariant will also be discussed. This is based on a joint work with Linsheng Wang.
40.
Time:11:00-12:00,Friday, June 14
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Shijin Zhang, Beihang University
Title:A quantitative second order estimate for p-harmonic functions in manifolds under curvature-dimension condition
Abstract:In this talk, first I will introduced some results about the gradient estimate of p-harmonic functions on Riemannian manifolds, including the results of Kotschwar-Ni, Wang-Zhang, Sung-Wang. Then I will introduce the results about the quantitative second-order Sobolev estimate of for positive p-harmonic functions in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions in weighted manifolds under the Bakry-Émery curvature-dimension condition. This is a joint work with Jiayin Liu and Yuan Zhou.
41.
Time:16:00,Friday, July 12
Venue:E4-201
Host:Xin Fu, ITS
Speaker:Song Dai, Tianjin University
Title:Existence of harmonic metrics on nilpotent Higgs bundles over noncompact Riemann surfaces
Abstract:In this talk, we will first introduce the notions of Higgs bundles and harmonic metrics. Then we will survey some known results on the existence of harmonic metrics over noncompact Riemann surfaces. Our new result is that given a generically regular nilpotent harmonic bundle, there exists a (unique) maximal harmonic metric on the corresponding graded Higgs bundle. We will sketch the proof and show some applications. This is a joint work with Qiongling Li.
42.
Time:10:00-11:00, Thursday, July 25
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Yaxiong Liu, University of Maryland
Title:The eigenvalue problem of complex Hessian operators
Abstract:In a very recent pair of nice papers of Badiane and Zeriahi, they consider the eigenvalue problem of complex Monge-Ampere and complex Hessian, and show that the C^{1,\bar{1}}-regularity of eigenfunction for MA and C^alpha-regularity for complex Hessian. They posed a question about the C^{1,1}-regularity of the eigenfunction and the uniqueness. We give a positive answer and show the C^{1,1}-regularity and uniqueness of the eigenfunction. We also derive a number of applications, including a bifurcation-type theorem and geometric bounds for the eigenvalue. This is a joint work with Jianchun Chu and Nicholas McCleerey.
43.
Time:14:00-15:00, Thursday, July 25
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Yueqiao Wu, John Hopkins University
Title:K-semistability of log Fano conesingularities
Abstract:K-stability of log Fano cone singularities was introduced by Collins-Sz\' ekelyhidi to serve as a local analog of K-stability of Fano varieties. In the Fano case, the result of Li-Xu states that to test K-stability, it suffices to test the so-called special test configurations. In this talk, I will talk about a local version of this result for log Fano cones. Our method relies on a non-Archimedean characterization of local K-stability. This is joint work with Yuchen Liu.
44.
Time:14:00-15:00, Thursday, August 1
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Chi Li, Rutgers University
Title:Kahler compactification of C^n and minimal discrepancy of Fano cone singularities
Abstract:Let X be a smooth complex manifold. Assume that Y ⊂ X is a Kahler submanifold such that X \ Y is biholomorphic to C^n. We prove that (X, Y ) is biholomorphic to (P^n, P^{n−1}). We also study certain Kahler orbifold compactifications of C^n and, as an application, prove that on C^3 the flat metric is the only asymptotically conical Ricci-flat Kahler metric whose metric cone at infinity has a smooth link. As a key technical ingredient, a new formula for minimal discrepancy of isolated Fano cone singularities in terms of generalized Conley-Zehnder indices in symplectic geometry is derived.
45.
Time:10:00-11:00, Wednesday, August 7
Venue:E4-201
Host:Jiyuan Han, ITS
Speaker:Gong Chen, Georgia Institute of Technology
Title:Recovery of the nonlinearity from the modified scattering map
Abstract:We consider the problem of recovering the nonlinearity in a nonlinear Schrödinger equation from scattering data, a problem for which there is a relatively large literature. We consider a new situation in which the equation does not admit standard scattering, but instead features the modified scattering behavior with logarithmic phase correction. We prove that even in this case, the modified scattering data suffices to determine the unknown nonlinearity. This is a joint work with J. Murphy (Oregon).
