Patrick Lei

This page contains notes that I took (by which I mean live-TeXed in almost all cases) during courses or seminars. If you find any mistakes in the notes, please email me or submit an issue (or pull request) on the git repository. Please note that the notes are not sorted in chronological order even within sections (instead, they are sorted roughly from less to more foundational).

Enumerative geometry
Title Date Location
Higher-genus GW theory of compact CY threefolds January 2025 SCGP
Enumerative invariants and birational geometry Spring 2024 Columbia
Simons summer math workshop Summer 2023 SCGP
integrability, enumerative geometry and quantization Summer 2022 SCGP
Informal enumerative geometry seminar Spring 2022 Columbia
Witten's conjecture Spring 2023 Columbia
Lines on cubic surfaces Spring 2022 Columbia
Other algebraic geometry
Title Date Location
Hyperbolicity Spring 2022 Columbia
Moduli spaces and hyperkähler manifolds Fall 2021 Columbia
Minimal model program Spring 2021 Zoom
Derived categories Spring 2022 Cornell
Hodge theory Fall 2021 Columbia
Deformation theory Fall 2021 Columbia
Intersection theory Spring 2021 Columbia
Geometric invariant theory Fall 2020 Columbia
FGA explained Fall 2020 Columbia
Schemes Spring 2021 Columbia
Varieties Spring 2019 UMass
Representation theory
Title Date Location
The count of instantons 2023-24 Columbia
DAHA and knot homology Fall 2021 Columbia
D-modules Spring 2022 Columbia
Category O Fall 2021 Columbia
Lie groups II Spring 2021 Columbia
Lie groups I Fall 2020 Columbia
Lie algebras Fall 2019 UMass
Representation theory Fall 2028 UMass
Algebra and number theory
Title Date Location
Class field theory Spring 2021 Columbia
Commutative algebra Fall 2020 Columbia
Algebra II Spring 2019 UMass
Topology
Title Date Location
Rational blowdowns Spring 2020 UMass
Complex cobordism Spring 2021 Columbia
Singular spaces Spring 2020 UMass
Algebraic topology II Spring 2021 Columbia
Algebraic topology I Fall 2020 Columbia
Symplectic topology Spring 2020 UMass
Manifolds Fall 2019 UMass
Analysis
Title Date Location
Real analysis II Spring 2019 UMass
Real analysis I Fall 2018 UMass
Complex analysis Fall 2019 UMass