Notes

These are short expository notes (most probably contain some typos).

Number theory

1. Local Class field theory via Lubin Tate Formal groups
2. Infinite Galois theory
3. Abelian varieties (coming soon)

Geometry

1. The Riemann-Roch theorem (coming soon)

Probability

1. On Choquet's theorem
2. Conformal Martingales, Brownian Martingales and Integral Representation
3. On Bessel processes
4. Burkholder-Davis-Gundy inequalities

Representation theory and Harmoic analysis

1. $p$-adic harmonic analysis
2. Introduction to modular representation theory of finite groups
3. A (very) brief introduction to symmetric spaces