# Garrett Brown

## About

I am a fourth 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:** 853 Evans Hall

**Email:** gm"my last name" at berkeley dot edu

**Office Hours:** Mondays 11am-noon in 959 Evans Hall (Math 56)

## Seminar

This semester I am organizing a learning seminar on the basics of the minimal model program in birational geometry.

## Research Interests and Papers

Some key phrases occurring in problems I am thinking about: extremal Kähler metrics, Kähler metrics with positive scalar curvature and relation with birational geometry, non-Kähler analogs, Hermitian Yang-Mills connections, and applications of complex geometry such as to minimal surfaces.

*The sign of scalar curvature on Kähler blowups* arXiv (2024). Submitted.
**Abstract:**
We show that if \((M,\omega)\) is a compact Kähler manifold with positive/negative scalar curvature, then the blowup of \(M\) at any point also furnishes a positive/negative scalar curvature Kähler metric in classes which make the exceptional divisor small. In the case of Kähler surfaces with positive scalar curvature, this extends a result of N. Hitchin to surfaces and answers a conjecture of C. LeBrun in the affirmative, as a result completing the classification of such surfaces.

## Upcoming/Recent Activities

Giving a talk at: Vanderbilt Geometry/Topology Seminar; September 27th; Vanderbilt University, Nashville, TN.
Participating in: Workshops on Geometric Analysis; August 19-December 20; SLMath (MSRI), Berkeley, CA.
## Other Links

With Thomas Browning, I have organized the Berkeley preliminary exam workshop for incoming and continuing math PhD students each semester since Fall 2022. The website for the Fall 2024 workshop can be found here.
REU Projects from undergrad.
Check out Vilas Winstein.
## Teaching Experience

**Fall 2024:** Head GSI for Math 56 with Professor David Nadler.
**Spring 2024:** Head GSI for Math 1B with Professor Alexander Paulin.
**Spring 2023:** GSI for Math 54 with Professor John Lott.
**Summer 2022:** Sole instructor for Math 54 lec 004.
**Fall 2021:** GSI for Math 54 with Professor David Nadler.