Below you may find various notes I have written for various purposes. If you wish to comment on them, please send me an email. I even like being notified of typos!

These are short notes mainly written to prove a short, self-contained result. No originality of the results is claimed (although I would be very happy if some of the proofs were novel).

- Fourier Transform of |
*x*|^{a} - Homogeneous Distributions and the Fourier Transform
- On Smoothing Operators
- Schwartz Kernel Theorem

- Fredholm Properties of Elliptic Operators
- Sharp Gårding Inequality
- Wavefront Set and Coordinate Invariance
- The Fundamental Theorem of Algebra using basic topology
- The Inverse Function Theorem and the Banach Fixed Point Theorem
- Jacobi's Formula and the Laplace-Beltrami Operator
- The Hodge Theorem and Pseudodifferential operators. Talk given at the MIT pure math student seminar, October 2016.

These are lecture notes from talks I have given.