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                      【理學院講壇】數學系學術報告
                      發布時間:2020-07-10【告訴好友】 【關閉窗口】

                        時間:2020/7/15 08:30-16:30

                        騰訊會議ID:184 504 216

                        會議主題:數學系學術報告

                        會議時間:2020/7/15 08:30-15:30

                        點擊鏈接入會,或添加至會議列表:

                        https://meeting.tencent.com/s/eyVFv6TqtBEB  

                        (一)報告人:劉佳堃 教授  澳大利亞臥龍崗大學

                        報告題目:Introduction to Optimal Transportation

                        報告摘要:

                        In this talk,we first give a brief introduction to the optimal transport problem,and then its extension to nonlinear case with application in geometric optics.Last,we introduce some recent results on the optimal partial transport problem,which is based on joint work with Shibing Chen (USTC) and Xu-Jia Wang (ANU).

                        (二)報告人:陳世炳 教授  中國科學技術大學

                        報告題目:On the four vertex theorem for curves on locally convex

                        報告摘要:

                        The classical four vertex theorem describes a fundamental property of simple closed planar curves.It has been extended to space curves,namely a smooth simple closed curve in $\mathbb{R}^3$ has at least four points with vanishing torsion if it lies on a convex surface.More recently,Ghomi extended this property to curves lying on locally convex surfaces.In this talk we will discuss an interesting approach using the regularity theory of Monge-Ampere equations.This is based on a joint work with Xu-jia Wang and Bin Zhou.

                       

                        (三)報告人:楊軍 教授  廣州大學

                        報告題目:Symmetric vortices for two-component $p$-Ginzburg-Landau systems 

                        報告摘要:Given $p>2$ for the following  coupled $p$-Ginzburg-Landau model in $\mathbb{R}^2$

                         -\Delta_p u^+ +\Big[A_+\big(|u^+|^2-{t^+}^2\big)  +A_0\big(|u^-|^2-{t^-}^2\big)\Big]u^+=0,

                        -\Delta_p u^- +\Big[A_-\big(|u^-|^2-{t^-}^2\big)  +A_0\big(|u^+|^2-{t^+}^2\big)\Big]u^-=0,

                        with the constraints

                        A_+, A_->0,  A_0^2<A_+A_- and t^+, t^->0,

                        we consider the existence of symmetric vortex solutions $u(x)=\big(U_p^+(r)e^{in^+\theta},U_p^-(r)e^{in^-\theta}\big)$ with given degree $(n^+, n^-)\in \mathbb {Z}^2$, and then prove the uniqueness and regularity results for

                      the vortex profile $(U_p^+, U_p^-)$ under more constraint of the parameters. Moreover, we also establish the stability result

                      for second variation of the energy around this vortex profile when we consider the perturbations in a space of

                      radial functions.

                            
                            
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