| Exotic algebraic models |
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| Hopf algebroids |
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| Adapted homology |
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| Universal homology |
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| Chromatic redshift |
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| Periodic torsion is torsion periodic |
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| Johnson-Wilson theory |
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| Stable $\infty$-categories |
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| The Adams spectral sequence |
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| Brown-Peterson cohomology |
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| Bousfield localization |
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| Complex cobordism cohomology |
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| The homotopy groups of the spheres, part 2 |
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| The homotopy groups of the spheres, part 1 |
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| The stable homotopy category |
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| Stable homotopy |
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| Formal group laws |
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| A first look at spectra |
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| Traveling |
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| On formal DG-algebras |
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| Tensor triangulated categories |
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| Updated geometric intuition |
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| Schemes |
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| Sha-algebras |
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| The associating homotopy |
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| Spaces with operations |
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| Homotopy associativity |
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| A lecture in my second year |
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| Hanging pictures with knots |
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| Are there knots? |
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| Quasi-categories |
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| Vertical monoids |
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| Equivalence of categories |
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| The homotopy litmus test |
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| Under category |
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| Defining the cosmos: Properties and definition |
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| Defining the cosmos: Enriched category theory |
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| The Warsaw circle |
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| Orbifolds |
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| Sheaves |
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| Swan’s theorem |
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| The homotopy category |
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| Homotopy in model categories |
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| Model categories |
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| Cofibrations |
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| Hanging pictures with homotopy |
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| A homotopy group of a sphere |
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| The Serre spectral sequence |
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| Homotopy groups |
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| Fiber bundles |
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| Fibrations |
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| More geometric intuition |
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| Geometric intuition |
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