## 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.

**2019**

**Number 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]