Subjects
A collection of notes I have written about various subjects. These were not written to be read by anyone but myself. I hope you find them useful, but use at your own risk.
Analysis [html] [pdf]Analytic number theory [html] [pdf]
Chromatic homotopy theory [html] [pdf]
Complex analysis [html] [pdf]
Continued fractions [html] [pdf]
Geometry of numbers [html] [pdf]
Group theory [html] [pdf]
Lie algebras [html] [pdf]
Riemannian geometry [html] [pdf]
Rings Modules Fields [html] [pdf]
Simplicial [html] [pdf]
Other
Miscellaneous notes I have written.
Multiplicative structures on spheres [html] [pdf]Invertibility hypothesis [html] [pdf]
Diagonal argument [html] [pdf]
Embeddings and Duality [html] [pdf]
Eulers Descent [html] [pdf]
Grobner Bases [html] [pdf]
Group Extensions [html] [pdf]
Morita Equivalence [html] [pdf]
Vector Bundles on P1 [html] [pdf]
PROMYS
Notes for talks I gave at PROMYS 2017-2019.
2019Number fields and the Laplacian [html] [pdf]
Local-Global Principle for nth Powers [html] [pdf]
The Hilbert Class Field [html] [pdf]
Lattices Quadratic Forms and Ideals [html] [pdf]
Fundamental Groupoids [html] [pdf]
Positive Definite Binary Quadratic Forms over Z [html] [pdf]
The Seifert Van Kampen Thoerem [html] [pdf]
2018
Poincare Homology Sphere [html] [pdf]
Crossing Numbers of Alternating Knots [html] [pdf]
Heegaard Splittings and Knots on the Torus [html] [pdf]
Morse Theory and Handles [html] [pdf]
Dehn Surgery and Kirby Calculus [html] [pdf]
Dimension and Moduli [html] [pdf]
Divisors and Intersections [html] [pdf]
Galois Theory and Riemann Surfaces [html] [pdf]
What is Algebraic Geometry [html] [pdf]
2017
Adjoints [html] [pdf]
But Dat Nullstellensatz Tho [html] [pdf]
Some Complex Theorems in Simple Analysis [html] [pdf]
Categories and Functors [html] [pdf]
Duality and Equivalences [html] [pdf]
Fundamental Groups and Covering Spaces [html] [pdf]
Natural Transformations [html] [pdf]
Representable Functors and the Yoneda Lemma [html] [pdf]
Universals and Limits [html] [pdf]
Academic projects
My senior thesis and junior paper at Princeton, as well as expository notes I have written for classes.
(Junior Paper) 3-Manifolds Knots and Homology 3-Spheres [html] [pdf](Senior Thesis) S3 pairs and Dehn surgery on Knots [html] [pdf]
2nd Order Elliptic PDE [html] [pdf]
Bott Periodicity and Clifford Algebras [html] [pdf]
Chern-Weil Gauss-Bonnet [html] [pdf]
Conjugacy of Cartan Subalgebras [html] [pdf]
Descent [html] [pdf]
Explicit Local Class Field Theory [html] [pdf]
Chern-Weil Gauss-Bonnet [html] [pdf]
K-Theory and Fredholm Operators [html] [pdf]
K-Theory and the Index Theorem [html] [pdf]
Morse Theory on Loop Spaces [html] [pdf]
Pontryagin Construction [html] [pdf]
Resolving Singularities Globally and Locally [html] [pdf]
Serre Spectral Sequence and the Homology of Loop Spaces [html] [pdf]