Garrett Brown

portrait

About

I am a third year math PhD student at UC Berkeley working with Song Sun. My interests lie in differential geometry/geometric analysis, usually in the setting of complex geometry. From Fall 2017 to Spring 2021, I was an undergraduate at Harvard College. Before that, I resided in southeast Michigan.

I am grateful for the support of an NSF Graduate Research Fellowship.

Office: 935 Evans Hall
Email: gm"my last name" at berkeley dot edu
Office Hours: None this semester

Research Interests and Papers

  • Special metrics in complex geometry: extremal Kähler metrics, Kähler metrics with positive scalar curvature, non-Kähler analogs.
  • Gauge theory in holomorphic vector bundles: Hermitian Yang-Mills connections, stable bundles, Kobayashi-Hitchin correspondence.
    1. The sign of scalar curvature on Kähler blowups arXiv (2024).

    Upcoming/Recent Conference Participation

  • New Frontiers in Curvature, Special Geometric Structures and Analysis; August 19-December 20; SLMath (MSRI), Berkeley, CA.
  • 4th Symposium on Geometry and Differential Equations; July 1-5; USTC Institute for Geometry and Physics, Hefei, China.
  • Aarhus Complex Geometry Workshop; June 24-27; Aarhus University, Aarhus, Denmark.
  • Geometry and Topology Conference; June 2-7; Qingtian, China.
  • Other Links

  • With Thomas Browning, I have organized the Berkeley math prelim workshop in Fall 2022, Spring 2023, Fall 2023, and Spring 2024. Materials can be found here.
  • REU Projects from undergrad.
  • Check out Vilas Winstein.