报告（一）题目：Marked Length Spectral determination of analytic chaotic billiards

报 告 人：Vadim Kaloshin教授(美国马里兰大学)

报告（一）时间：2023年8月21日星期一上午10:00-12:00

报告（一）形式：数理楼135报告厅

报告（一）摘要：We consider billiards obtained by removing from the plane three strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides natural labeling of periodic orbits. Jointly with J. De Simoi and M. Leguil, we show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of all obstacles. For obstacles without symmetry assumption, V. Otto recently showed that the Marked Length Spectrum along with information about two obstacles determines the geometry of all remaining obstacles.

报告（二）题目：Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem

报 告 人：Vadim Kaloshin教授(美国马里兰大学)

报告（二）时间：2023年8月22日星期二上午9:00-11:00

报告（二）形式：数理楼135报告厅

报告（二）摘要：We shall discuss the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun--Jupiter--asteroid systems. It is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. An important parameter is the ratio between square root of the mass ratio and eccentricity of Jupiter. We shall discuss the results of Wisdom, Neishtadt and others in one regime and the results joint with Fejoz, Guadria, Martin in the other.

个人简历：Vadim Kaloshin，美国马里兰大学-帕克分校数学系Brin首席教授、奥地利科技学院讲席教授，欧洲科学院院士，曾获得美国科学院院士提名、西蒙斯奖等荣誉，现担任Adv. Math., Ergodic Theory Dynam. Systems等杂志编委，且在2004-2019年曾担任数学四大杂志之一Invent. Math.的编委，主要从事动力系统领域的研究，在国际上最顶尖的四大综合性数学期刊Acta Math., Ann. of Math., J. Amer. Math. Soc., Invent. Math.上公开发表高质量学术论文9篇，在Duke Math. J., Geom. Funct. Anal., J. Eur. Math. Soc (JEMS), Comm. Pure Appl. Math., Arch. Ration. Mech. Anal.等国际权威期刊上公开发表高水平学术论文65篇。