学术报告
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The Dual Minkowski Problem for Symmetric Convex BodiesThe dual Minkowski problem asks for the necessary and sufficient conditions on a given measure $/mu$ so that it can be realized as the dual curvature measure of a convex body. Just like the classical Minkowski problem, the dual Minkowski problem reduces to Monge-Ampere type equation. However, in this talk, we shall solve the dual Minkowski problem for $o$-symmetric convex bodies directly for measures using variation of calculus. The solution is closely connected to a measure concentration condition.Zhao Yiming C.L.E. moore instructor(Massachusetts Institute of Technology)致远楼101室2019 年 06 月04 日 10:00-11:00
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KL-Cells in the Weighted Coxeter GroupsKazhdan-Lusztig cells in the weighted Coxeter groups was first introduced systematically by Lusztig in 2003. He propose a bundle of conjectures on the cells in order to generalize some results from the equal parameter case to the unequal parameter case. In this talk, I intend to give a brief introduction on the topic and report some recent achievements concerning the description of cells.时俭益 教授 (华东师范大学)致远楼108室2019年6月3日 16:00-17:00
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On Gaussian Curvature Equation with Nonpositive CurvatureWe present some results concerning the solutions of $$ /Delta u +K(x) e^{2u}=0 /quad{/rm in}/;/; /mathbb{R}^2 $$ with $K/le 0$. We introduce the following quantity: $$/alpha_p(K)=/sup/left/{/alpha /in /R:/, /int_{/R^2} |K(x)|^p(1+|x|)^{2/alpha p+2(p-1)} dx<+/infty/right/}, /quad /forall/; p /ge 1.$$ Under the assumption $({/mathbb H}_1)$: $/alpha_p(K)> -/infty$ for some $p>1$ and $/alpha_1(K) > 0$, we show that for any $0 < /alpha < /alpha_1(K)$, there is a unique solution $u_/alpha$ with $u_/alpha(x) = /alpha /ln |x|+ c_/alpha+o/big(|x|^{-/frac{2/beta}{1+2/beta}} /big)$ at infinity and $/beta/in (0,/,/alpha_1(K)-/alpha)$.Furthermore, we show an example $K_0 /leq 0$ such that $/alpha_p(K_0) = -/infty$ for any $p>1$ and $/alpha_1(K_0) > 0$, for which we prove the existence of a solution $u_*$ such that $u_* -/alpha_*/ln|x| = O(1)$ at infinity for some $/alpha_* > 0$, but does not converge to a constant at infinity.周风 教授 (华东师范大学 偏微分方程中心)致远楼101室2019年6月1日 星期六 下午 13:30-14:30
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Mean Curvature Flow of Surfaces in a Hyperkaehler 4-ManifoldIn this talk, we firstly prove that every hyper-Lagrangian submanifold L^{2n}(n > 1) in a hyperkaehler 4n-manifold is a complex Lagrangian submanifold. Secondly, we study the geometry of hyper-Lagrangian surfaces and demonstrate an optimal rigidity theorem with the condition on the complex phase map of self-shrinking surfaces in R^4 . Last but not least, we show that the mean curvature flow from a closed surface with the image of the complex phase map contained in S^2/(S^1_{+}) in a hyperkaehler 4-manifold does not develop any Type I singularity. This is a joint work with Dr. Linlin Sun.邱红兵 副教授(武汉大学)致远楼101室2019 年 05 月31 日 9:30-10:30
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Einstein-Like Property of Focal Submanifolds of Isoparametric Hypersurfaces i...In this talk, we first show that the focal submanifolds of isoparametric hypersurfaces with g=4 distinct principal curvatures in the unit sphere are Willmore submanifolds of the sphere. Furthermore, we classify which of them are Einstein or Einstein-like. As a byproduct, we give simply connected examples of the Besse problem.彦文娇 教授 (北京师范大学)致远楼101室2019 年 05 月31 日 16:00-17:00
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Isoparametric Polynomials and Sums of SquaresWe introduce a recent joint work with Prof. Zizhou Tang on nonnegative polynomials induced from isoparametric polynomials. We completely solve the question that whether they are sums of squares of polynomials, giving infinitely many explicit examples to Hilbert's 17th problem as well as some applications.葛建全 教授 (北京师范大学)致远楼101室2019 年 05 月31 日 15:00-16:00
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On L_p Dual Minkowski ProblemWe will introduce the L_p dual surface measure (recently defined by Huang- Lutwak-Yang-Zhang in Adv. Math. 2018). Then we will discuss the related L_p dual Minkowski problems in integral and convex geometry.周家足 教授 (西南大学)致远楼101室2019年5月31日14:00-15:00
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Geometric Flows to Minkowski ProblemsIn this talk, we recall how to solve Minkowski problems by using geometric flows, such as Gauss curvature flow. In particular, a recent joint work, the regularity of Lp dual Minkowski problem with Chuanqiang Chen, Yiming Zhao will be particularly discussed.黄勇 教授 (湖南大学)致远楼101室2019年05月31日 10:30-11:30