学术报告
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S-Closed Conformal Transformations in Finsler GeometryWe will introduce the S-closed conformal transformation in Finsler geometry. We show some properties of such transformation. Using some results, we show how to refine a rigidity theorem of Matsumoto problem about conformally equivalent between two non-Riemannian Berwald manifolds.沈斌 副教授 (东南大学)腾讯会议室2021年10月26日 10:00-11:00
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Deformations of Q-CurvatureQ-curvature is 4th-order analog of scalar curvature, which is an important geometric object in the study of conformal geometry. In this talk, after reviewing some of our previous work about deformations of Q-curvature, I will talk about some new progresses in the study of the volume comparison result of Einstein manifolds with respect to Q-curvature. This series of works are joint with Yueh-Ju Lin in Wichita State University.袁伟 教授 (中山大学)腾讯会议室2021年10月26日 09:00-10:00
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Huber's Theorem for Conformally Compact ManifoldsLet Ω be a domain of a closed manifold $(M, g_0)$ with dim M>2. Let $g=u^\frac{4}{n-2}g_0$ be a complete metric defined on Ω. We will show that $M\setminus Ω$ is a finite set when $\int_Ω|Ric(g)|^\frac{n}{2}dV_g<+∞. Such a result is not true if we replace Ricci curvature with Scalar curvature. We will discuss the properties of conformal metrics with $\|R\|_{L^\frac{n}{2}}<+∞$ on a punctured ball of a Riemannian manifold , and give some geometric obstacles for Huber's theorem in this case.李宇翔 教授 (清华大学)腾讯会议室2021年10月26日 08:00-09:00
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Applications of Potential Theory in Differential GeometryAs is well known, potential theory is a useful tool to study PDE. In this talk, I will briefly show that how to apply it to study conformal geometry and hypersurfaces in hyperbolic spaces. There are joint works with Professor Jie Qing at UCSC.马世光 副教授 (南开大学)致远楼101室2021年10月22日 10:30-11:30
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Rigid/Extremal of Scalar CurvatureAs a curvature of riemannian manifold, like the sectional curvature and the Ricci curvature, there are topology and geometry results about the scalar curvature. In this talk, we talk the rigid/extremal property of scalar curvature which is proposed by Gromov in his “Four lectures on scalar curvature“.孙昱凯 博士 (华东师范大学)宁静楼117室2021年10月22日 13:30-15:00
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Gradient Estimates and Liouville Theorems for Lichnerowicz EquationsWe study the positive solutions to a class of general semilinear elliptic equations ∆u(x) + uh(ln u) = 0 defined on a complete Riemannian manifold (M, g) with Ric(g) ≥ −Kg, and obtain the Li-Yau type gradient estimates of positive solutions to these equations which do not depend on the bounds of the solutions and the Laplacian of the distance function on (M, g). We also obtain some Liouville-type theorems for these equations when (M, g) is noncompact and Ric(g) ≥ 0 and establish some Harnack inequalities as consequences. Then, as applications of main theorem we extend our techniques to the Lichnerowicz-type equations黄平亮 教授 (上海大学)致远楼101室2021年10月21日 10:30-11:30
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Symmetrized Data Aggregation for FDR ControlWe develop a new class of distribution–free multiple testing rules for FDR control. I will mainly illustrate the idea via multiple testing with general dependence. A key element in our proposal is a symmetrized data aggregation (SDA) approach to incorporating the dependence structure via sample splitting, data screening and information pooling. The SDA substantially outperforms the knockoff method in power under moderate to strong dependence, and is more robust than existing methods based on asymptotic p-values. I will also talk about some other applications, such as the selection of the number of change-points and threshold selection in feature screening.邹长亮 教授 (南开大学)腾讯会议室2021年10月21日 20:00-21:00
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Some Wall-Crossing Techniques in Enumerative GeometryThe theory of Gromov-Witten invariants is a curve counting theory defined by integration on the moduli of stable maps. Varying the stability condition gives alternative compactifications of the moduli space and defines similar invariants. One example is epsilon-stable quasimaps, defined for a large class of GIT quotients. When epsilon tends to infinity, one recovers Gromov-Witten invariants. When epsilon tends to zero, the invariants are closely related to the B-model in physics. The space of epsilon's has a wall-and-chamber structure. In this talk, I will explain how wall-crossing helps to compute the Gromov-Witten invariants and sketch a proof of the wall-crossing formula.周扬 青年研究员(上海数学中心)宁静楼115室2021年10月15日 上午10:00-11:00