Notes $\def\Z{\mathbb Z} \def\Q{\mathbb Q} \def\C{\mathbb C} \def\Torelli{\mathcal I}$

These are some miscellaneous notes I have written. They are not intended for publication and for the most part do not contain original material.

pdf  abs Half lives, half dies and the signatures of boundaries

pdf  abs Calculus: the greatest hits

pdf  abs Tiling rectangles by squares

pdf  abs Harmonic functions on finite graphs

pdf  abs The Cauchy-Binet formula

pdf  abs Existence and uniqueness for integral curves

pdf  abs Tychonoff's theorem

pdf  abs Burnside's paqb-theorem

pdf  abs Algebraicity of matrix entries of representations

pdf  abs Representations of products

pdf  abs The Jacobson density theorem

pdf  abs Identifying primes in polynomial time: the AKS algorithm

pdf  abs The representation theory of SLn($\Z$)

pdf  abs Knot complements and Spanier-Whitehead duality

pdf  abs Periodic billiard paths on smooth tables

pdf  abs My favorite proof of the Pythagorean Theorem

pdf  abs Smith theory and Bredon homology

pdf  abs Hopf's theorem via geometry

pdf  abs Spines of manifolds and the freeness of fundamental groups of noncompact surfaces

pdf  abs The word problem for surface groups and hyperbolic geometry

pdf  abs Lie groups and automatic continuity

pdf  abs Two nonstandard constructions of free groups

pdf  abs Classifying spaces and Brown representability

pdf  abs Representation theory without character theory

pdf  abs The symplectic representation of the mapping class group is surjective

pdf  abs Realizing homology classes by simple closed curves

pdf  abs The action of the deck group on the homology of finite covers of surfaces

pdf  abs The Noetherianity of group rings

pdf  abs One-relator groups

pdf  abs A quick proof of the Seifert-Van Kampen theorem

pdf  abs The isoperimetric inequality in the plane

pdf  abs The generalized Schoenflies theorem

pdf  abs Homotopy groups of spheres and low-dimensional topology

pdf  abs The complex of cycles on a surface (after Bestvina-Bux-Margalit)

pdf  abs The Torelli group and congruence subgroups of the mapping class group

pdf  abs Rochlin's theorem on signatures of spin 4-manifolds via algebraic topology

pdf  abs The congruence subgroup problem for SLn($\Z$)

pdf  abs The fundamental theorem of projective geometry

pdf  abs The Borel density theorem

pdf  abs The action on homology of finite groups of automorphisms of surfaces and graphs

pdf  abs A quick proof of the classification of surfaces

pdf  abs The abelianization of the level L mapping class group