《科学大讲堂 理学院 第257期》Malabika Pramanik 教授：方向有多分散？稀疏性、树状结构和极大算子

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• 题目: 方向有多分散？稀疏性、树状结构和极大算子
• 主讲人：Malabika Pramanik 教授 @ 不列颠哥伦比亚大学
• 时间：2026年10月14日 16:30
• 地点：理学院一楼1142报告厅

主讲人简介

Professor Malabika Pramanik is a professor at the University of British Columbia, and director of the Banff International Research Station (BIRS) in Canada. She obtained a PhD in 2001 from the University of California, Berkeley, supervised by Michael Christ. Since then, she has made great contributions to modern harmonic analysis and geometric measure theory, and was an invited speaker at the International Congress of Mathematicians in 2022. She is a fellow and currently a vice-president of the American Mathematical Society, contributing greatly to community outreach and supporting inclusion and diversity in mathematics.

讲座简介

Directional maximal operators average a function over long, thin rectangles whose orientations are drawn from a prescribed set of directions. Their analytic behaviour depends in subtle ways on the geometric and combinatorial structure of that set: sufficiently sparse, or lacunary, families yield bounded operators, while richer direction sets can generate Kakeya-type phenomena and dramatically different estimates.In this talk, I will describe a tree-based framework for measuring the complexity of a set of directions. The central invariant, called the splitting number, records the extent of persistent branching in the associated direction tree. I will explain its connection with classical notions of finite-order lacunarity and show how this perspective leads naturally to estimates for directional maximal operators. The resulting picture brings together harmonic analysis, geometric measure theory, and combinatorics, and provides a useful language for distinguishing genuinely lacunary direction sets from those capable of supporting Kakeya-type constructions.This is joint work with Edward Kroc and Juyoung Lee.

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