Kimball Strong

Kimball Strong | Notes

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A calculation of the cohomology rings of real and complex projective spaces, starting by proving the Leray-Hirsch Theorem for fibre bundles, and then specializing to the Thom class of a vector bundle: Cohomology of projective spaces.

Slides from a presentation I gave at the end of a course on topological theory. It followed a presentation on the Serre-Swan Theorem, and was meant to motivate algebraic K-theory of a ring: Algebraic Vector Bundles and K-Theory

A topological proof that every nontrivial monotone graph property on a prime power number of vertices is evasive. Written as a final project with Chase Vogeli for an Analysis of Algorithms class: Evasiveness

Notes on spectral sequences made in preparation for my A-Exam, which was pronounced "least computational spectral sequences talk I've ever seen" by my advisor. The first introduces the concept of a spectral sequence with some unorthodox basic examples, and the other two are about particular spectral sequences. Knowledge of the Serre Spectral sequence is required to fully understand the latter two.