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 study symplectic geometry and Floer theory. Right now, I mainly think about using Floer-theoretic invariants to study symplectic embeddings and dynamical problems. I also am interested in low-dimensional topology, gauge theory, and homotopy theory, and their relations to Floer 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 Symplectic Camel and Spaces of Symplectic Embeddings, Berkeley Symplectic and Contact Geometry Seminar, April 2024. (Notes)
  

• Generalized Cohomology Operations and the Atiyah–Hirzebruch Spectral Sequence, Berkeley Spectra Seminar, February 2025. (Notes)
  

• Structures on Manifolds and the Triangulation Conjecture, Berkeley Student Low-Dimensional Topology Seminar, Feburary 2025. (Notes)
  

• Minimal Genus Problems in 4-Manifolds, Berkeley Student Low-Dimensional Topology Seminar, October 2024. (Notes)
  

• The Seiberg–Witten Equations and Gradient Flow, Berkeley Symplectic and Contact Geometry Seminar, October 2024. (Notes)
  

• The PSS Isomorphisms and Maps in Hamiltonian Floer Theory, Berkeley Symplectic and Contact Geometry Seminar, April 2024. (Notes)
  

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

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

Expository Notes

I took my qualifying exam in November 2024. You can find my syllabus and transcript here. While studying, I wrote notes on my topics (symplectic geometry, algebraic topology, and elliptic PDEs) which can be found here.

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
  

Conferences Attended/Upcoming

• Workshop on Moduli Spaces of Pseudo-Holomorphic Curves, Oneonta, New York, May 2025.
  
• Winter School on Enumerative Geometry and Mirror Symmetry, Caltech, Pasadena, January 2025.
  
• Hot Topics: Life after the Telescope Conjecture, SL Math, Berkeley, December 2024.
  
• Rutgers Symplectic Summer School, Rutgers University, New Brunswick NJ, August 2024.
  

• 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.