学术报告
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The Isoperimetric Inequality in the 2-Dim Finsler Space FormsIn this talk, I will introduce the Finsler geometry and the background of the isoperimetric problem. By using the variational theory, we give the local solution of the isoperimetric problem in 2-dimensional Finsler space forms. This is the joint work with Mengqing Zhan.周林峰 副教授 (华东师范大学)宁静楼 104 室2019 年 03 月27 日 15:00-16:00
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Kahler-Ricci Flow on Fano BundlesIn this talk, I first recalled some knowledge of the Kahler-Ricci flow. Then I will talk about the behavior of the Kahler-Ricci flow on some Fano bundles which is a trivial bundle on one Zariski open set. We show that if the fiber is $/mathbb{P}^{m}$ blown up at one point and the initial metric is in a suitable kahler class, then the fibers collapse in finite time and the metrics converge sub-sequentially in Gromov-Hausdorff sense to a metric on the base. In the talk, I will aim to talk about in the case of product manifolds. This is a joint work with Xin Fu.张世金 博士 (北京航空航天大学)宁静楼 104 室2019年03月27日 16:00-17:00
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Analysis on Area-Minimizing Hypersurfaces in ManifoldsLet N be an (n+1)-dimensional complete manifold of Ricci curvature≥-n, and B_2 (p) be the geodesic ball in N. Let M be an area-minimizing hypersurface in B_2 (p) with p∈M and ∂M⊆〖∂B〗_2 (p). In this talk, we will discuss the Sobolev and Neumann-Poincare inequalities on M∩B_1 (p). As an application, we get the gradient estimates for the solutions of the minimal hypersurface equation on an n-manifold with Ric≥-(n-1).丁琪 博士 (复旦大学)宁静楼 104 室2019 年 03 月27 日 14:00-15:00
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Some Conjectures about Column LLT PolynomialsColumn LLT polynomials are well-studied symmetric functions defined by Lascoux, Leclerc and Thibon. Column LLT polynomials are Schur positive, and they have many nice combinatorial properties. We conjecture that column LLT polynomials are e-positive when substituting q with 1+q, and the coefficients of the e-basis expansion can be obtained by constructions of "inequality" graphs.邱敦 博士(University of California San Diego)致远楼101室2019年3月26日(周二)上午10-11点
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On Orbit BraidsLet $M$ be a connected topological manifold of dimension at least 2 with an effective action of a finite group $G$. Associated with the orbit configuration space of the $G$-manifold $M$, we give the notion of orbit braids and define the orbit braid group. We further study the subgroups of orbit braid group and various relations among these subgroups with the fundamental groups of the configuration spaces given by the manifold $M$ with or without the $G$-action, and the $M/G$. We also calculate the orbit braid groups in the plane with two typical actions. This talk is based upon the joint work with Hao Li and Fengling Li.吕志 教授(复旦大学 探花视频 )致远楼101室3月26日 下午3:30-4:30
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On A Conjecture of Toponogov on Complete Convex SurfacesIn 1995, Victor Andreevich Toponogov authored the following conjecture: “Every smooth strictly convex and complete classical surface of the type of a plane has an umbilic point, possibly at infinity“. In our talk, we will outline a proof, in collaboration with Brendan Guilfoyle. Namely we prove that (a) the Fredholm index of an associated Riemann Hilbert boundary problem for holomorphic discs is negative, which is an outcome of the regularity of the Cauchy-Riemann operator in presence of a symmetry group. Thereby, (b) no such solutions may exist for a generic perturbation of the boundary condition (these form a Banach manifold under the assumption that the Conjecture is incorrect).Wilhelm Klingenberg (Durham University)致远楼101室2019年3月25日 星期一 15:00-16:00
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τ-Tilting Finiteness of Two-Point Algebrasτ-tilting theory was introduced by Adachi, Iyama and Reiten, which completes the classical tilting theory from the viewpoint of mutation. They constructed a class of Λ modules named (support) τ-tilting modules, where Λ is a finite dimensional basic algebra over an algebraically closed field. We call Λ a τ-tilting finite algebra if there are finitely many isomorphism classes of basic τ-tilting Λ-modules. In this talk, we explain τ-tilting theory by discussing the τ-tilting finiteness of two-point algebras. More precisely ,we will show the poset structure on the set of support τ-tilting modules, the bijection between support τ-tilting modules and two-term silting complexes, etc,.Qi Wang (Osaka University)致远楼108室2019年3月19日 4:00pm —5:00pm
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九维流形上的切触结构在本报告中,我将给出九维流形上存在切触结构的充分必要条件。该结果是与墨尔本大学Diarmuid Crowley合作完成的。杨会军(河南大学)致远楼101室2019年3月15日16:15-17:15