notes

(The writings below are broadly related to geometry. Some are informal notes and may not have been fully checked.)

Noncommutative geometry and operator algebras

K-theory of the Roe algebra, a working note.

Crossed Products, Groupoids, and the Irrational Rotation Algebra, study notes.

The Atiyah–Hirzebruch Vanishing Theorem, notes for a talk in the Noncommutative Geometry Seminar.

Tomita–Takesaki Theory, notes from the Groundwork for Operator Algebras Lecture Series, given by Brent Nelson.

Subfactors, notes from a special lecture at the Groundwork for Operator Algebras Lecture Series, given by Emily Peters.

Scalar curvature

Notes on positive scalar curvature, reading notes.

Geometry and topology

A Discussion on Analytic Web Geometry, written for a graduate algebraic geometry course.

Admissible \(A_p\) Weights on Harmonic NA Groups, notes for a talk in a graduate harmonic analysis course.

Morse Homology and Instanton Floer Homology, notes from two short talks in a graduate Gauge Theory course.

Grassmannian, Flag, and Schubert Varieties, notes for a talk in the graduate course “Topics in Combinatorics: Symmetric Functions”.

Haefliger’s Theorem and Novikov’s Theorem in Codimension 1, notes for a talk in the Szegő Seminar, the graduate student seminar.