Princeton University

Department of Mathematics · Geometric Measure Theory

United States · PhD

The Department of Mathematics at Princeton University has a world-class tradition in geometric measure theory, encompassing minimal surfaces, geometric variational problems, fractal geometry, and related areas. It is a top-tier academic institution for research on geometric aspects of the Kakeya conjecture.

学术历史

Princeton's geometric measure theory tradition is closely associated with the work of Frederick Almgren, Ernst Reifenberg, and other scholars. Almgren made foundational contributions to minimal surface theory and geometric measure theory. The university has long maintained a world-leading position in geometric analysis and the calculus of variations, providing a deep foundation for geometric research on the Kakeya problem.

当前状态

The Department of Mathematics currently offers courses in geometric measure theory, minimal surfaces, differential geometry, and related areas, with active seminars in geometry and analysis. The university's close collaborative relationship with the Institute for Advanced Study (IAS) provides students with additional academic resources.

实验室 / 研究中心

Princeton Mathematics Department - Geometry

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关键人物

Fernando Codá Marques

Professor

Expert in differential geometry and geometric measure theory, with significant contributions to minimal surfaces, Morse theory, and geometric variational problems. In collaboration with Neves, he achieved breakthroughs on the Willmore conjecture and other problems.

André Neves

Professor

Expert in differential geometry who, in collaboration with Marques, made multiple breakthrough contributions in minimal surface theory and geometric measure theory, including the resolution of the Willmore conjecture.

标志性成果

Almgren's foundational work on minimal surfaces and geometric measure theory
Marques and Neves's breakthrough on the Willmore conjecture and related problems
Princeton's Department of Mathematics has consistently ranked among the top three globally in QS/THE mathematics rankings