**Geometric Analysis seminar talk list:**

**1.**

**Time: **14:00-15:00, Tuesday, January 9

**Venue:** E4-201

**Speaker:** Xingzhe Li, Cornell University

**Title: **Generic Scarring for Minimal Hypersurfaces in Manifolds Thick at Infinity with a Thin Foliation at Infinity

**Abstract:** In this talk, we present a generic scarring phenomenon for minimal hypersurfaces in a class of complete non-compact manifolds. In particular, for generic metrics on manifolds thick at infinity with a thin foliation at infinity, to each closed stable minimal hypersurface, there exists a sequence of closed minimal hypersurfaces, with area diverging to infinity, that accumulate along the stable hypersurface.

**2.**

**Time:** 15:30-16:30, Tuesday, January 9

**Venue:** E4-201

**Speaker:** Xuan Yao, Cornell University

**Title: **Applications of level set method in dimension 3

**Abstract:** In this talk, we introduce some recent developments in the applications of level set method in dimension 3, especially in the study of positive scalar curvature problems.

**3.**

**Time:** 10:30-11:30, Friday, January 19

**Venue:** E4-201

**Speaker: **Liding Huang, Xiamen University

**Title: **The stability of generalized Kahler Ricci Flow on toric Fano manifolds

**Abstract:** To construct canonical metrics and understand existence and moduli problems in generalzized Kahler geometry, Streets-Tian introduce the generalized Kahler-Ricci flow. We will discuss the stability of generalized Kahler Ricci Flow on toric Fano manifolds.

**4.**

**Time:** 9:00-10:30, Monday, March 4

**Speaker: **Jintian Zhu, Westlake University

**Title: **Positive scalar curvature metrics and aspherical summands

**Abstract:** In this talk, we consider obstruction for complete positive scalar curvature metrics on the aspherical summands $N\# X$ in dimensions up to five, where is $N$ a closed aspherical manifold and $X$ is an arbitrary non-compact manifold. We start by recalling related backgrounds as well as the slice-and-dice argument by Chodosh and Li, and then we show how to prove our main theorem with their techniques after introducing several essential improvements. This work is joint with Dr. Shuli Chen from Stanford University and Prof. Jianchun Chu from Peking University.

**Tencent Meeting: **760 6725 7412

**Passcode: **678332

**5.**

**Time:** 9:00-11:00, Monday, March 11

**Speaker: **Xiaoshang Jin, Huazhong University of science and technology

**Title: **Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below

**Abstract:** We establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with $Ric \geq -n g$ It extends the classic result of Argostianiani, Fogagnolo and Mazzieri to the Riemannian manifold of negative curvature. As an application, we construct a Willmore-type inequality for closed hypersurfaces in hyperbolic space and obtain the characterization of geodesic sphere. This is a joint work with Jiabin Yin.

**Tencent Meeting: **760 6725 7412

**Passcode: **678332

**6.**

**Time:** 9:00-10:30, Monday, March 18

**Speaker:** Chao Li, NYU

**Title: **Stable minimal hypersurfaces in R^5

**Abstract: **In this talk, I will explain why a complete stable minimal hypersurface in R^5 is flat. This is based on joint work with Chodosh, Minter and Stryker.

**ZOOM ID：**952 802 9961

**Password：**314159

**7.**

**Time:** 13:00, Thursday, March 21

**Venue:** E4-201

**Speaker:** Zexuan Ouyang, Peking University

**Title: **Metric SYZ of Fermat type hypersurface

**Abstract: **In this talk, we investigate the behavior of the Calabi-Yau metrics of the Fermat family near the large complex structure limit. In particular, we will demonstrate that the SYZ conjecture holds in the Fermat case to some extent. This talk is based on the work of Yang Li.

**8.**

**Time:** 9:00, Friday, March 22

**Speaker:** Tong Freid, Havard University

**Title: **Monge Ampere equations and complete Calabi Yau metrics

**Abstract: **I will discuss a new free-boundary problem for a real Monge-Ampere equations that arises from the study of Calabi-Yau metrics. This is based on joint work with T. Collins and S.-T. Yau.

**ZOOM ID：**952 802 9961

**Password：**314159

**9.**

**Time:** 13:00, Friday, March 22

**Venue:** E4-201

**Speaker:** Song Yujian, Peking University

**Title: **Classification of gravitational instanton

**Abstract: **Gravitational instantons were introduced by Hawking in 1977. Mathematically, they are complete, non-compact hyperKahler 4-manifolds with curvature decay. It has been conjectured that there exist 4 main families of gravitational instantions according to their asymptotics by Cherkis and Kapustin. In 2022, this problem was solved by Sun and Zhang by using metric geometry and PDE analysis, resulting 6 different families (ALE,ALF, ALG, ALG*, ALH, ALH*). They study the collapsing limit of hyperKahler manifolds, and give an explicit description of the limit space. In particular, this calculates the asymptotic cones of gravitational instantons. In this talk, we will give a brief introduction about gravitational instantons. And then we discuss Sun–Zhang's work about the classification.

**10.**

**Time:** 9:00-11:00, Monday, March 25

**Venue:** E4-201

**Speaker:** Ruiming Liang, Peking University

**Title: **Asymptotically locally Euclidean metric with holonomy SU(m)

**Abstract: **In this talk, we first review the Eguchi-Hanson metric which is a typical example of ALE manifold. Generalizing the example, a calabi type conjecture for ALE manifolds can be stated. I'll explain the approach to address this problem following D.Joyce's paper.

**11.**

**Time:** 9:00-11:00, Tuesday, March 26

**Venue:** E4-201

**Speaker:** Linsheng Wang, Nanjing University

**Title: **Stable degenerations of klt singularities

**Abstract: **In this talk, I will introduce Xu-Zhuang's proof of finite generation result with respect to the associated ring of the normalized volume minimizer, which finishes the proof of stable degeneration conjecture of klt singularities.

**12.**

**Time:** 14:00-16:00, Wednesday, March 26

**Venue:** E4-201

**Speaker:** Shengxuan Zhou, Peking University

**Title: **Gromov-Hausdorff limits with large homology

**Abstract: **In this talk, we will introduce the Gromov-Hausdorff limit constructed by Hupp-Naber-Wang. In their construction, the limit space has dense topological singularities.

**13.**

**Time:** 9:00-11:00, Wednesday, March 27

**Venue:** E4-201

**Speaker:** Minghao Miao, Nanjing University

**Title: **On a Sufficient Criterion for the existence of cscK metrics

**Abstract: **In this talk, we will survey K. Zhang's work on a sufficient criterion for the existence of cscK metrics. We will discuss criteria for uniform J-stability as an intermediate step.

**14.**

**Time:** 14:00-15:00, Wednesday, March 27

**Speaker:** Bin Zhou, Peking University

**Title: **Regularity of variational problems with a convexity constraint

**Abstract: **We establish the interior $C^{1,\alpha}$ regularity of minimizers of a class of functionals with a convexity constraint, which includes the principal-agent problems studied by Figalli-Kim-McCann. The $C^{1,1}$ regularity was previously proved by Caffarelli-Lions in an unpublished note when the cost is quadratic, and recently extended to the case where the cost is uniformly convex with respect to a general preference function by McCann-Rankin-Zhang(arXiv:2303.04937). Our main result does not require the uniform convexity assumption on the cost function. In particular, we show that the solutions to the principal-agent problems with $q$-power cost are $C^{1,\frac{1}{q-1}}$ when $q > 2$ and $C^{1,1}$ when $1<q\leq 2$. Examples can show that this regularity is optimal when $q\geq 2$.

**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: **TBA

**Abstract: **TBA