Notes

Sometimes I like to write things.

INFORMAL NOTES

• Party hats and explosions: An introduction to blowups in algebraic geometry from a classical perspective (and comparison with the scheme-theoretic approach), with the worked-out example pf the blowup of an affine cone.


• Projective embedding of proper algebraic curves: A friendly and liesurely exposition of the ideas behind the Riemann-Roch theorem, in the classical setting of compact Riemann surfaces.


• Baby's First Riemann-Roch: An informal and hopefully friendly exposition about embedding (smooth proper) algebraic curves into projective spaces.


• Introduction to Enumerative Geometry: Notes from a minicourse on basic intersection theory and applications to enumerative questions in algebraic geometry. Following the book 3264 & All That, Intersection Theory in Algebraic Geometry by Eisenbud-Harris.


• Tangent space to a character variety: A little note made for a geometric group theorist about the moduli-theoretic (algebraic-geometry-like) computation of the tangent space of a character variety.


• "What is an electron?" or, Particles as represetations: Informal notes on how elementary particles may be viewed as irreducible unitary representations. No prior knowledge of physics assumed, not likely acquirable by reading this either.


• Grothendieck and Springer's New Year resolutions for 2019 : Informal notes on the Grothendieck resolution and the Grothendieck-Springer resoltuion.


• Spectra Are Your Friends: A Leisurely Stroll Through the Land of Spheres : Very informal notes on basic stable homotopy theory. In progress!

SLIGHTLY LESS INFORMAL NOTES

• Monodromy determines a local system : A short note on a silly ∞-categorical proof of the classical fact that a local system is entirely determined by its monodromy representation.


• Grothendieck Spectral Sequence in Higher Algebra : Some notes on constructing certain spectral sequences.


• Concise summary of some ∞-abstract nonsense : Due to an - expletive deleted - policy at my old university, I had to write an appendix on everything that I used in the main body of my Masters thesis, that was not part of the regular curriculum. What resulted was a blitzkrieg through parts of HTT, HA, and SAG - use at your own peril!