Gabriel Beiner

Department of Mathematics, University of California, Berkeley
Office: 935 Evans Hall
Email: [first name] dot [last name] at berkeley.edu

I am a second year math PhD student at UC Berkeley supervised by Michael Hutchings. My undergraduate degree is from the University of Toronto. I am interested in symplectic geometry and its relations to low-dimensional topology and mathematical physics. This has included studying topics like Floer theory, gauge theory, and index theory.

Research

• Failure of $L^p$ Symmetry of Zonal Spherical Harmonics, with William Verreault, Journal of Spectral Theory (2023).

• Getzler Rescaling and Symbol Calculus in Local Index Theory Via Weightings on Vector Bundles, NSERC undergraduate research supervised by Eckhard Meinrenken.

Talks

• The PSS Isomorphisms and Maps in Hamiltonian Floer Theory, Berkeley Symplectic and Contact Geometry Seminar, April 2024. (Handwritten Notes... covering a lot more than my talk)
  

• The Casson Invariant and Instanton Floer Homology for Homology 3-Spheres, Berkeley Student 3-Manifold Seminar, February 2024. (Handwritten Notes)
  

• Chern-Simons Theory and the Wess-Zumino-Witten Model, Berkeley Student 3-Manifold Seminar, November 2023. (Handwritten Notes)
  

Expository Notes

As I prepare for my qualifying exam this year, I have been making comprehensive notes on symplectic geometry, algebraic topology, and PDEs. My completed notes on algebraic topology can be found here (please let me know about any serious typos).

I also have some notes written during my undergrad that may be of interest to others. Read at your own risk.

• The ADHM Construction
  
• The Yang-Mills Equations
  
• The Wheeler-DeWitt Equation
  

Teaching

Berkeley

• Math 1A: Calculus, Fall 2023, Summer 2024 (Head GSI), Fall 2024.

Toronto

• MAT244: Introduction to Ordinary Differential Equations, Fall 2022.
• MAT246: Concepts in Abstract Mathematics, Spring 2022 (some problems I wrote for the class).
• MAT188: Linear Algebra, Fall 2020.