【学术预告】数学与统计学学院学术预告四则
报告题目1：onvariationalproblems ofquantummany-bodysystems
报告人：郭玉劲
报告地点：数学楼315会议室
报告摘要：The variational problems are often used to model the ground states of quantum many-body systems, including ultracold Bose gases, ultracold Fermi gases, pseudo-relativistic boson stars, and so on. The interactions among atoms represents a major difficulty in mathematically understanding such quantum systems. The investigations on the corresponding variational problems can be traced back as early as the celebrated works of P.L. Lions and E. Lieb around 1980s. In this series of talks, we shall first introduce the fundamental main results of several typical variational problems.We then discuss how to analyze the limiting behavior of the variational problem arising in ultracold Bose gases. The variational problems in the rotational case is finally analyzed.
报告人简介：郭玉劲，教授，博士生导师，华中师范大学数学与统计学学院副院长，先后主持中国科学院“百人计划”、国家自然科学基金优秀青年科学基金、国家杰出青年科学基金等项目。主要从事变分理论及其在非线性偏微分方程、数学物理等领域的应用研究，围绕微机电系统MEMS方程、质量临界约束变分理论、量子多体系统涡旋现象等课题做出过一系列原创性研究。相关成果在美国数学会出版一部英文研究专著，在Comm. Pure Appl. Math.、Arch. Ration. Mech. Anal.、Trans. Amer. Math. Soc.、J. Math. Pure Appl.等数学权威期刊上发表论文40余篇。
报告题目2：Pohozaev type identities and their applications. Topic II: Concentrated solutions to nonlinear Schrodinger equations with very degenerate potentials.
报告人：彭双阶
报告时间：8月19日（周六下午）15:00-18:30
报告地点：数学楼315会议室
报告摘要：Part I:In this talk, we first introduce the Pohozaev identities, and then apply them to study the singularly perturbed problems and elliptic problems for the uniqueness results and the existence of infinitely many solutions.
PartII:We talk about a type of singularly perturbed nonlinear Schrodinger equation with a potential and obtain a more accurate location for the concentrated points, the existence and the local uniqueness for positive multi-peak solutions when the potential possesses non-isolated critical points by using the modified finite dimensional reduction method based on local Pohozaev identities. Moreover, for several special potentials, with its critical point set being a low-dimensional ellipsoid, or a part of hyperboloid of one sheet or two sheets, we obtain the number and symmetry of multi-peak solutions by using local uniqueness of concentrated solutions. Here the main difficulty comes from the different degenerate rate along different directions at the critical points of the potential. This is a joint work with Peng Luo, Kefan Pan and Yang Zhou.
报告人简介：彭双阶，教授、华中师范大学党委常委、副校长、博士生导师。2011年获得国家杰出青年科学基金，2012年入选首批“湖北省高端人才引领培养计划”。曾获得教育部自然科学二等奖和湖北省自然科学奖特（一）等奖，国家级教学成果奖二等奖。先后主持了国家自然科学基金重点项目、教育部“长江学者与创新团队”发展计划项目等。共发表学术论文100余篇，其中多篇论文发表在Adv.Math.、J.Math.Pures.Appl.、Proc. London Math.Soc.、Tran. Amer. Math. Soc.、Math.Ann、 Arch. Ratinal. Mech.Anal.、 Ann.I.H.Poincaré- AN等重要学术期刊上，其研究成果引起了国内外专家的广泛关注，被美国、德国、意大利、澳大利亚等国家的数学家大量引用或推广，并用来解决其它的问题。
报告题目3：Dynamic behaviors of a Leslie-Gower model with strong Allee effect and fear effect in prey
报告人：陈玉明
报告时间：8月21日（周一下午）15:30-18:30
报告地点：数学楼315会议室
报告摘要：In this talk, we study the dynamics of a Leslie-Gower model with Allee effect and fear effect in prey.The origin is an attractor,which implies that the ecological system collapses at low densities. Qualitative analysis reveals that both effects are crucial in determining the dynamics behaviors of the model.There can be different types of bifurcations such as saddlenode bifurcation,non-degenerate Hopf bifurcation with a simple limit cycle,degenerate Hopf bifurcation with multiple limit cycles,Bogdanov-Takens bifurcation,and homoclinic bifurcation.
报告题目4：Some novelties in applying Lyapunov’s direct method
报告人：陈玉明
报告时间：8月22日（周二下午）9:00-12:00
报告地点：数学楼315会议室
报告摘要：The global stability of equilibria of epidemic models plays an important role in understanding the underlying disease transmission mechanisms. One of the most powerful approaches to determine global stability is Lyapunov’s direct method. The method involves constructing an appropriate Lyapunov function and verifying negative (semi-)definiteness of its derivative along solutions, which often are not easy to achieve. This talk reports some new ideas on applying Lyapunov’s direct method. On the one hand, a new kind of function for constructing Lyapunov functions is given. On the other hand, a new procedure to determine whether a given Lyapunov function candidate works or not is developed. The procedure consists of a novel way to rearrange the terms of the derivative along solutions.
报告人简介：陈玉明，加拿大罗瑞尔大学(Wilfrid Laurier University)数学系教授、博士生导师。主要研究兴趣为动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用。在SIAM Journal on Mathematical Analysis，Journal of Differential Equations，Proceedings of the American Mathematical Society，Mathematical Biosciences等国际著名刊物发表论文150余篇，其成果被同行广泛引用，曾获安大略省科技与创新部早期研究者奖。先后主持5项加拿大国家自然科学与工程理事会(NSERC)科研基金项目，参与3项中国国家自然科学基金面上项目。