I'm a graduate student in mathematics at UC-Berkeley. I like teaching, I like algebraic topology, and I'm getting better at both. I was an undergraduate student in computer science at UIUC from 2005 to 2009, and I stayed one extra year to work with Matt Ando, who taught me a whole lot about topology. I've since moved to Coolifornia, where I've started working with Constantin Teleman, though I've been sort of doing my own thing. We have vague plans of using Morava E-theories to study his TQFTs valued in finite homotopy types.
I will be a visiting student at MIT for the Spring 2013 semester.
I'm currently interested in using algebro-geometric tools to answer questions in algebraic topology, and I have a penchant for computations.
I've tried to get into the habit of keeping a big tree of all the things I'd like to think about. It's incomplete and largely nonsensical, but you can find an HTML copy of it here: [link].
I passed my qualifying exam on November 23rd, 2011. Here is a PDF containing my syllabus and a transcript of the exam questions I could remember: [link].
I'm not very active, but I have also written some things on MathOverflow.
I'm funded through a GSI position, so I run recitation sections for a few lower-level courses. Students and onlookers can find course pages below. I also have a calendar available at this address to facilitate setting up meetings and so forth. I've also started participating in seminars; you can find those below too.
|Agenda:||A small agenda program, written in OCaml, to keep track of deadlines and so forth, though its feature list has grown marginally from those beginnings.|
|Ext Chart:||A utility in development for drawing and computing with spectral sequences.|
|Smithy:||A map editor, also written in OCaml, for the Marathon engine, a game from the mid '90s now actively developed under the name Aleph One.|
|MW2:||A small collection of thoughts on reverse-engineering some of the engine and data pieces in Activision's classic MechWarrior 2.|
|Op:||A rewrite system in Mathematica to determine the closure of a set of cohomology classes in H^*(K(Z, n); Z/2) under the action of the Steenrod algebra. Useful for expanding Singer's and Stong's calculations of H^*(BU<2k>; Z/2).|
|Coact:||Mathematica package for computing the free and square-zero parts of the coaction of the dual Steenrod algebra on the space of multiplicative k-variate cocycles.|
|A-cocycles:||Mathematica package for computing the space of additive cocycles, along with some of the tertiary invariants described in our paper.|
|A-visual:||Mathematica notebook with some graphical routines, displaying some of the tertiary invariants in our paper. Used in a presentation to Stephen Wolfram.|
|M-cocycles:||Mathematica package for computing obstructions to free extension from the tangent space of multiplicative cocycles to the total space. Doesn't completely work, but it's close, and it's complete enough to warrant sharing. Missing backtracking, mostly.|
This is a work in progress.