Math 696

Winter Term 2026

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Math 696
Algebraic Topology II
Homological stability

Student Explainer Videos

For their final projects in Math 696, students created the folloiwng "Explainer videos". These are introductory videos on topics in algebraic topology, pitched at the level of a student who has completed a first course in algebraic topology (such as Math 592).

Zhiqing Chen	I: Cohomology II: The Čech complex III: Derived functors IV: Line bundles
Colin Feeney	Steenrod squares
Nick Freeman	Abelian categories
Atharva Gawde	Topological K-theory
Gahl Shemy	The Leray–Serre spectral sequence
Ajay Srinivasan	Spectra
Bailee Zacovic	The Serre duality theorem (corrigenda)
	There are two errors on the slide deriving the algebraic genus of a nonsingular projective curve. First, we omit our implicit assumption that C is irreducible. Second, under this assumption, the fact that dim H^0(C, O_C) = 1 holds in general, whereas the cohomology argument presented only applies to plane curves.
Steve Zanetti	Obstruction theory
Jacob Zweifler	The spectral sequence of a double complex

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