University of California, Los Angeles

Department of Mathematics, Harmonic Analysis Direction

United States · PhD

The UCLA Department of Mathematics is a world-leading center in harmonic analysis, centered on Terence Tao and encompassing restriction theory, Kakeya estimates, additive combinatorics, and analytic number theory. It is one of the most important academic institutions for research on the Kakeya conjecture.

学术历史

UCLA's harmonic analysis tradition was established by Christopher Herz and later scholars including Terence Tao. Tao made several important contributions to the Kakeya conjecture from the late 1990s to the early 2000s, including methods developed in collaboration with Wolff and the resolution of the finite field Kakeya problem. Tao was awarded the Fields Medal in 2006, with part of the work directly related to the Kakeya problem.

当前状态

The UCLA Department of Mathematics currently offers specialized courses in harmonic analysis, additive combinatorics, and analytic number theory, with Professor Tao leading multiple research projects. The department houses an Analysis Group that holds regular seminars in analysis and number theory. PhD students can participate in cutting-edge topics such as Kakeya estimates, restriction theory, and additive combinatorics.

实验室 / 研究中心

关键人物

标志性成果

• Tao's breakthrough work on Kakeya estimates (1990s–2000s)
• Tao awarded the Fields Medal (2006), with part of the work related to the Kakeya problem
• Important progress on the finite field Kakeya problem
• Bourgain-Guth improvement in restriction theory

学术资源

证据