2017年中国复分析会议系列报告

报告人：崔贵珍研究员（中科院数学与系统科学研究院）

报告题目：Parabolic implosion surgery and twist deformation of rational maps

报告摘要：Consider the Riemann surfaces of a geometrically finite rational map. A repeated Dehn twist will produce a sequence of rational maps in its moduli space. We will prove that this sequence is convergent under certain condition. The proof involves iteration on Teichmuller spaces and a surgery perturbation which realize a parabolic implosion.

报告时间：9月23日上午9:15-10:15

报告地点：孔子会堂

报告人简介：崔贵珍，1992获北京大学博士，然后在中国科学院数学与系统科学研究院工作至今。主要研究方向为：单复分析，Teichmuller空间，复动力系统。与他人合作对Thurston关于临界有限有理函数的刻画推广到任意双曲有理函数，从而解决McMullen提出的一个问题。曾主持基金委重点项目和杰出青年基金。

2017年中国复分析会议系列报告

报告人：李琼玲博士后（加州理工学院）

报告题目：Cyclic Higgs bundles and minimal surfaces

报告摘要：Given a G-Higgs bundle over a closed Riemann surface, there is a unique equivariant harmonic map from the universal cover of the Riemann surface into the associated symmetric space of G. We find a maximum principle theorem for a type of coupled linear elliptic systems and apply it to analyze the Hitchin equation for cyclci Higgs bundles. In this case, the harmonic map is conformal and hence minimal. We show several domination results of the pullback metrics of the branched minimal immersion. We also discuss the case Riemann surface with punctures, for example, the uniqueness of harmonic maps.

报告时间：9月24日上午8:30-9:30

报告地点：香格里拉酒店二楼青岛厅

报告人简介：李琼玲，2014获莱斯大学博士，然后在丹麦奥胡斯QGM研究所和加州理工数学院担任联合博士后至今。主要研究方向为：Teichmuller空间，调和映照，Higgs丛。与他人合作对cyclic Higg丛渐进性的分析研究，解决在cyclic Higgs 丛情形下Katzarkov-Noll-Pandit-Simpson关于Hitchin WKB 问题的猜想。

2017年中国复分析会议系列报告

报告人：尤建功教授（南开大学）

报告题目：Quasi-perodic operators and quasi-periodic cocycles

报告摘要：Quasi-periodic operators has strong background in quantum physics. The eigenvalue equations of the operators define a familyof quasi-periodic cocycles onof the form . The full understanding of the dynamics of  this family of cocycles will lead to full understanding of the corresponding operators. In the talk, I will give a brief survey on this topic and present our recent results on the Dry Ten Martini Problem, Aubry-Andre-Jitomirskaya conjecture. The talk is based on joint works with Avila and Zhou.

报告时间：9月25日上午8:30-9:30

报告地点：香格里拉酒店二楼青岛厅

报告人简介：尤建功，1983年毕业于徐州师范学院，1989年获北京大学理学博士学位，1989-1991年在南京大学做博士后，1991年起历任南京大学讲师、副教授、教授、博士生导师、长江学者、数学系主任，2016年起任南开大学陈省身数学研究所教授、博士生导师。曾在德国科隆大学和慕尼黑工大做洪堡学者；曾访问瑞士苏黎世高工(ETH)数学研究所等多所国外著名大学。在Duffing方程的稳定性，KAM理论，哈密顿偏微分方程的拟周期运动、薛定谔算子的谱理论等方面做出了一系列深刻的工作。曾获得国家杰出青年基金、香港求是科技基金会杰出青年学者奖、中国高校科技进步奖一等奖（排名第二）、第六届江苏省青年科技奖、国家自然科学二等奖（排名第三）。现承担国家基金委重点项目和国家重大基础研究规划项目。

2017年中国复分析会议系列报告

报告人：Walter Bergweiler professor（ Christian-Albrechts-University of Kiel）

报告题目：Radially distributed values and normal families

报告摘要：We consider functions holomorphic in the unit disk for which all zeros lie on one ray while all one-points lie on a different ray. We show that the family of all these functions is normal in the unit disk punctured at the origin. The case where the zeros are positive and the one-points are negative is studied in more detail. The results are joint work with Alexandre Eremenko.

报告时间：9月26日上午8:30-9:30

报告地点：香格里拉酒店二楼青岛厅

报告人简介：Walter Bergweiler’s main research area is complex analysis. One topic he is particularly interested in is complex dynamics. This is concerned with the behavior of complex-valued functions under iteration. For example, one studies for which starting values the sequence of iterates converges, whether it has convergent subsequences, etc. The dependence on parameters other than the starting value is also of interest. The corresponding subsets of the complex plane are usually very complicated and they are appealing also to the non-mathematician. Some of these pictures are collected in a gallery. But the mathematics behind them is much more beautiful than the pictures! Other topics in complex analysis where he is interested in are the theory of entire and meromorphic functions, differential and functional equations in the complex domain, quasiregular maps in higher dimension and normal families.