Gabriel Beiner

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

I am a third year math PhD student at UC Berkeley supervised by Michael Hutchings. My undergraduate degree is from the University of Toronto. I study symplectic and contact geometry. I mainly think about using pseudoholomorphic curve invariants and Floer theory to understand symplectic dynamics and symplectic/contact topology. I'm also interested in gauge theory, low-dimensional topology, and other types of dynamical flows.

I am a co-organizer for Kylerec 2026 on link spectral invariants and Weyl Laws.

Last semester I organized a student Floer seminar on symplectic field theory.

I am keeping a list of sources in Floer homology here.

Research

Infinite ECH capacities and Anosov flows, (arxiv).
Failure of L^p symmetry of zonal spherical harmonics, with W. Verreault, Journal of Spectral Theory (journal).

Expository Talks and 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.

Talk Notes

Generating functions and singular support, Baby GRT Seminar, April 2026. (Notes)
Extracting invariants from SFT, Berkeley SFT Seminar, November 2025. (Notes)
The Atiyah–Floer conjecture for admissible bundles, Berkeley Student Low-Dimensional Topology Seminar Seminar, October 2025. (Notes)
Generic transversality in SFT, Berkeley SFT Seminar, October 2025. (Notes)
Bredon cohomology and Smith theory, Berkeley GRT Seminar, September 2025. (Notes)
String topology and its role in Floer theory, Berkeley Symplectic and Contact Geometry Seminar, September 2025. (Notes)
Introduction to SFT, Berkeley SFT Seminar, August 2025. (Notes)
Open-closed and closed-open maps, Kylerec, May 2025. (Notes)
The geometry of log smooth manifolds, Workshop on Moduli Spaces of Pseudo-Holomorphic Curves, May 2025. (Notes)
The Bauer–Furuta invariant and 10/8, Berkeley Student Low-Dimensional Topology Seminar, April 2025. (Notes)
The symplectic camel and spaces of symplectic embeddings, Berkeley Symplectic and Contact Geometry Seminar, March 2025. (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, February 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)