学术报告报告主题: Function Spaces, Curves and Vanishing Classes in Quasiconformal Teichm\uller Theory
报 告 人: 陶菲
报告时间：2026年 10月26日，28日，30日，11月1日（周一、三、五、日）下午3：00-4:00
报告地点：腾讯会议：99267619381
邀 请 人: 何遵武 副教授
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数学学院
2026年10月23日
报告摘要：
Many subspaces of the universal Teichm\uller space can be described in three equivalent ways. They correspond to function spaces of holomorphic functions, to classes of quasisymmetric homeomorphisms, and to geometric classes of quasicircles. In each description one finds a bounded class together with its vanishing subclass, such as the Bloch space and the little Bloch space, $\mathrm{BMOA}$ and $\mathrm{VMOA}$, or quasicircles and asymptotically conformal curves. This lecture series studies how these vanishing conditions correspond to each other.
The first lecture extends Pommerenke’s characterizations of little Bloch and $\mathrm{VMOA}$ functions to conformal maps of the half-plane. The key step is the introduction of geometric notions relative to the boundary parametrization. The second lecture constructs an asymptotically conformal chord-arc curve which is not asymptotically smooth. This shows that $\mathrm{VMOA}$ is strictly smaller than $\mathrm{BMOA}\cap B_0$, and it leads to a new intermediate Teichm\uller space between the $\mathrm{BMO}$ and $\mathrm{VMO}$ Teichm\uller spaces. The third lecture introduces graph weldings and relates Zygmund, $\mathrm{BMO}$, $\mathrm{VMO}$ and $H^{1/2}$ regularity of a function to the regularity of the boundary correspondence. It also proves that every graph domain is a $\mathrm{BMO}$ domain, and it realizes the above gap by explicit graphs. The fourth lecture shows that weak asymptotic symmetry implies asymptotic symmetry for quasisymmetric embeddings of the real line and for homeomorphisms between quasilines under natural geometric assumptions. This answers a question of Brania and Yang.
报告人介绍：
陶菲，现任北京大学北京国际数学研究中心（BICMR）博雅博士后。2023年起加入北京国际数学研究中心从事博士后研究工作。自2025年4月起，受聘访问日本早稻田大学，与 Matsuzaki 教授开展合作研究。
陶菲博士的研究方向主要为复分析理论与 Teichmüller 空间，深入探讨拟共形映射、Muckenhoupt 权理论、万有 Teichmüller 空间的 BMO 理论等重要课题。相关研究成果已在 Sci. China Math.、Rev. Mat. Complut.、Proc. Amer. Math. Soc.、Acta Math. Sin. (Engl. Ser.) 等国内外重要数学期刊发表多篇论文。