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] [abstract] Calculus: the greatest hits

[pdf] [abstract] Tiling rectangles by squares

[pdf] [abstract] Harmonic functions on finite graphs

[pdf] [abstract] The Cauchy-Binet formula

[pdf] [abstract] Existence and uniqueness for integral curves

[pdf] [abstract] Tychonoff's theorem

[pdf] [abstract] Burnside's paqb-theorem

[pdf] [abstract] Algebraicity of matrix entries of representations

[pdf] [abstract] Representations of products

[pdf] [abstract] The Jacobson density theorem

[pdf] [abstract] Identifying primes in polynomial time: the AKS algorithm

[pdf] [abstract] The representation theory of SLn($\Z$)

[pdf] [abstract] Knot complements and Spanier-Whitehead duality

[pdf] [abstract] Periodic billiard paths on smooth tables

[pdf] [abstract] My favorite proof of the Pythagorean Theorem

[pdf] [abstract] Smith theory and Bredon homology

[pdf] [abstract] Hopf's theorem via geometry

[pdf] [abstract] Spines of manifolds and the freeness of fundamental groups of noncompact surfaces

[pdf] [abstract] The word problem for surface groups and hyperbolic geometry

[pdf] [abstract] Lie groups and automatic continuity

[pdf] [abstract] Two nonstandard constructions of free groups

[pdf] [abstract] Classifying spaces and Brown representability

[pdf] [abstract] Representation theory without character theory

[pdf] [abstract] The symplectic representation of the mapping class group is surjective

[pdf] [abstract] Realizing homology classes by simple closed curves

[pdf] [abstract] The action of the deck group on the homology of finite covers of surfaces

[pdf] [abstract] The Noetherianity of group rings

[pdf] [abstract] One-relator groups

[pdf] [abstract] A quick proof of the Seifert-Van Kampen theorem

[pdf] [abstract] The isoperimetric inequality in the plane

[pdf] [abstract] The generalized Schoenflies theorem

[pdf] [abstract] Homotopy groups of spheres and low-dimensional topology

[pdf] [abstract] The complex of cycles on a surface (after Bestvina-Bux-Margalit)

[pdf] [abstract] The Torelli group and congruence subgroups of the mapping class group

[pdf] [abstract] Rochlin's theorem on signatures of spin 4-manifolds via algebraic topology

[pdf] [abstract] The congruence subgroup problem for SLn($\Z$)

[pdf] [abstract] The fundamental theorem of projective geometry

[pdf] [abstract] The Borel density theorem

[pdf] [abstract] The action on homology of finite groups of automorphisms of surfaces and graphs

[pdf] [abstract] A quick proof of the classification of surfaces

[pdf] [abstract] The abelianization of the level L mapping class group