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Course Notes:

Quantum Mechanics and String Theory (Fall 2022): Graduate course taught by Paul Aspinwall of Duke. INCOMPLETE (illness).

Commutative Algebra (Fall 2022): Graduate course taught by Prakash Belkale of UNC-CH. INCOMPLETE (illness).

Algebraic Geometry (Spring 2022): Graduate course taught by Shrawan Kumar of UNC-CH. INCOMPLETE (lost the folder with my notes in it :/).

Complex Geometry (Fall 2020): Graduate course taught by Bernd Siebert of UT Austin. Covers lots of Huybrechts, including Hodge theory, Kahler geometry and sheaf theory.

Symplectic Topology (Fall 2020): Graduate course taught by Tim Perutz of UT Austin. Includes symplectic manifolds, Hamiltonian mechanics and some bundles and characteristic classes. INCOMPLETE.


An Example a Day Directory (Started Spring 2023): “I do an example every day”, where each word in that sentence is left up to interpretation.

Differentiability of Lipschitz Functions (Rademacher’s Theorem) (Fall 2022): Final presentation for the measure theory course at UNC-CH. An overview of the proof of Rademacher’s Theorem: Lipschitz functions in R^n are differntiable a.e.

Introduction to Derived Functors (Fall 2022): Final presentation for the commutative algebra course at UNC-CH. Introduces derived functors, Ext/Tor, and an interesting calculation of Ext groups.

The Derived Category of Coherent Sheaves (Fall 2022): A 2 part talk given at jGMRT seminar at UNC-CH providing an introduction to D^b(Coh(X)), as well as some interesting applications cited without proof.

Categorical Representation Theory (Spring 2022): Online seminar/mini-course taught by Gurbir Dhillon as part of the Yale algebra and geometry series centered on an introduction categorical representation theory and the Langlands program. Here is the organizing website link. IN PROGRESS.

Introduction to Kahler Geometry and Hodge Theory (Spring 2022): Final presentation for the algebraic geometry course at UNC-CH. Truthfully this talk has nothing to do with AG though, it is all differential geometry.