Resources

This is a slightly chaotic archive of notes I’ve accumulated over the years. They’re mostly for my own reference, but a wandering student might find something useful (or at least interesting) along the way.

⚠️ Fair warning: very little of this has been carefully fact-checked - proceed with curiosity and a healthy dose of skepticism!

Symplectic and Contact

Constructions in Symplectic and Contact Topology Notes [pdf]
(Compiled from a seminar I ran in Spring 2025)
Legendrian Knot Surgery Notes [pdf] (Comparison of descriptions common in literature)
Legendrian Differential Algebra and Contact Homology Notes [pdf]

Low Dimensional Topology

Knot Theory Lecture Notes [pdf]
(Part III Lecture notes, Cambridge, Spring 2022)
Knot Theory Precis [pdf]
(Part III, Cambridge, Spring 2022)

Morse Homology Lecture Notes [pdf] (Based on Hutchings, Spring 2023)
The Alexander Polynomial [pdf]
(Algebraic Topology, Fall 2022)
Simply-connected, Spineless 4-Manifolds [pdf]
(Part III Essay, Cambridge, Spring 2022)

Miscellaneous

Talk notes on Donaldson's 4-6 Question [pdf]
(For SSSSS UC Berkeley 2025, referencing a talk by Amanda Hirschi at GITC 2025)
Introductory Note on 3D Weinstein Conjecture [pdf]
(GITC 2025, Dan Cristofaro-Gardiner)
Introductory Note on Branched Covers [pdf] (GITC 2025, Tye Lidman)
Note on Nonseparating 2-Spheres [pdf] (UC Berkeley)
Milnor's Exotic Spheres [pdf] [slides] (University of Edinburgh, Spring 2021)

Assorted Graduate Notes

Finite Dimensional Lie and Associative Algebras Notes [pdf]
(Part III Lecture notes, University of Cambridge, Fall 2021)
Finite Dimensional Lie and Associative Algebras Precis [pdf]
(Part III, University of Cambridge, Fall 2021)
Symplectic Geometry Precis [pdf]
(Intended for Qualifying Examination Preparation, UC Berkeley 2024)
Differential Geometry [notes.pdf] [precis.pdf]
(Part III Lecture notes, University of Cambridge, Spring 2022)
Complex Differential Geometry [notes.pdf]
(Part III Lecture notes, University of Cambridge, Spring 2022)
Coxeter Groups [notes.pdf] [precis.pdf]
(Part III Lecture notes, University of Cambridge, Spring 2022)
Algebraic Topology Precis [pdf]
(Part III Lecture notes, University of Cambridge, Fall 2021)

Assorted Undergraduate Notes

Algebraic Geometry Precis [pdf]
(University of Edinburgh, 2020-2021)
Algebraic Topology Precis [pdf]
(University of Edinburgh, 2020-2021)
Geometry of General Relativity Precis [pdf]
(University of Edinburgh, 2020-2021)
Group Theory Precis [pdf]
(University of Edinburgh, 2020-2021)
Galois Theory Precis [pdf]
(University of Edinburgh, 2020-2021)
Linear Analysis Precis [pdf]
(University of Edinburgh, 2020-2021)
Honours Analysis Notes [pdf]
(University of Edinburgh, 2019-2020)
Honours Complex Analysis Precis [pdf]
(University of Edinburgh, 2019-2020)
Honours Linear Algebra Precis [pdf]
(University of Edinburgh, 2019-2020)

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