时间:2025年3月4日(星期二)16:00-17:30
地点:E10-212
主持人: 理论科学研究院 Ivan Fesenko
主讲人: 香港大学 莫毅明
主讲人简介:莫毅明教授为香港大学谢仕荣卫碧坚基金教授(数学)、数学系讲座教授及数学研究所所长。他是中国科学院院士、香港科学院院士及美国数学学会院士。
莫教授于1978年获耶鲁大学文学硕士学位,1980年获斯坦福大学博士学位,随即在普林斯顿大学开始教学及研究生涯。随后,他担任哥伦比亚大学及巴黎大学(奥赛)教授,并于1994年回港出任香港大学数学系讲座教授。
莫教授的研究领域包括多复变函数、复微分几何、代数几何及函数超越论。1988年,他解决了凯勒几何中的广义弗兰克尔猜想,这是半正曲率情况下的均匀化定理的高维类似物。他与 J.-M. Hwang 一起发展了单规则射影流形上最小有理切线 (VMRT) 簇的一般理论,并用它来解决一系列与此类流形有关的代数几何经典开放问题,特别是解决了拉扎斯菲尔德问题并证明了紧致型不可约厄米对称空间在凯勒变形下的刚性。2019年,他与 J. Pila 和 J. Tsimerman 一起建立了期待已久的志村簇 Ax-Schanuel 定理,该定理已经在数论的核心问题(例如与有理点有关的问题)上得到了惊人的应用。
莫教授的编辑职责包括2002年至2014年担任《数学发明》杂志的编辑委员会成员。2010年,他担任国际数学家大会 (ICM) 菲尔兹奖委员会成员。他担任2023-2025年邵逸夫数学奖评选委员会成员。莫教授目前担任香港数学学会名誉会长。
莫教授曾获多项学术殊荣,包括1984年斯隆奖学金、1985年美国总统青年科学家奖、1998年香港裘槎杰出学者奖、2007年国家自然科学奖、2009年美国数学会伯格曼奖、2022年国际华人数学家大会陈省身奖、2022年未来科学大奖(数学与计算机科学)及2022年陈嘉庚数学与物理学奖。
报告题目:Bounded Symmetric Domains, Shimura Varieties and Beyond
摘要:Bounded symmetric domains Ω are bounded Euclidean realizations of Hermitian symmetric spaces of the semisimple and noncompact type. As such they are of immediate research interest from the perspectives of several complex variables and complex differential geometry. On the other hand, quotients of bounded symmetric domains by lattices of automorphisms correspond to moduli spaces for various classification problems. Especially, Shimura varieties, which are quotients of bounded symmetric domains by arithmetic lattices, have been of central interest in different research areas of number theory and algebraic geometry. From the perspective of complex geometry, quotient manifolds by torsion-free lattices have been studied as complex manifolds admitting geometric structures and Kähler metrics with special curvature properties, and as such the lattices need not be arithmetic.
In this lecture, the speaker will trace his path of research in part with collaborators on bounded symmetric domains, Shimura varieties and beyond, going over various rigidity phenomena and characterization theorems and exhibiting the cross-fertilization of perspectives and methodologies in the study of such classical spaces, including complex differential geometry (Gauss-Bonnet formulas, Kähler metrics, curvature asymptotics, holomorphic isometries), several complex variables (Hartogs phenomenon, L^2-estimates of ∂ˉ, closed positive currents), partial differential equations (the ∂ˉ-equation, the Poincaré-Lelong equation and its analogues, the complex Monge-Ampère equation), harmonic analysis (Fatou’s theorem on bounded holomorphic functions, non-tangential limits), algebraic geometry (Chow schemes on compact duals Ω^, universal families and quotients of their restrictions to Ω), o-minimal theory (counting theorems, tame complex geometry) and dynamical systems (foliations, ergodic theory, renormalization). If time permits we will explore the interface between bounded symmetric domains Ω and the theory of varieties of minimal rational tangents (VMRTs) modeled on their compact duals Ω^.
