# David Spivak

Research Scientist
Department of Mathematics
MIT

Email: dspivak--math/mit/edu

Metric realization. A short paper (possibly with errors) connecting fuzzy simplicial sets and metric spaces, by way of adjoint functors.

Smooth chess. A short, unfinished paper about something I call "smooth chess," in which the idea is to generalize chess by replacing the set {0,1} with the unit interval [0,1].
So, on your turn, you can move fractional pieces adding up to 1. For example .7 white bishop moves to a square with .4 black queen and thereby captures .1 of the black queen (the square now contains .7 white bishop and .3 black queen). In the same turn, white also moves .3 pawn, and thus his total move is .7+.3=1, as desired. Fractional pieces (e.g. rooks) can move through squares that are already inhabited by other fractional pieces, so long as they do not "overflow the square" in doing so.

Stokes Theorem A look at freshman vector calculus from the perspective of differential geometry. (Written as a grad student.)

My PhD thesis. The 150 page version that preceded the current version.

Grothendieck Topologies Another way to view Grothendieck topologies.

Box monads. An unfinished note about two monads I like on the category of categories.

Presheaf the cobbler A funny abstract for a talk I gave about presheaves and sheaves.

Group-ring calculation program. An object-oriented program I wrote in the "Scheme" programming language, which solves equations in groups, rings, group-rings, etc. Very un-user-friendly. Runs in emacs.

Sheaves and Homotopy Theory Dan Dugger's unpublished paper on sheaves and homotopy theory.

A quote of Albert Einstein on the importance of the theory of knowledge. I got this from Ronnie Brown.

symbols.pdf LaTeX symbols.

symbols-all.pdf Many more LaTeX symbols

xyguide.pdf A guide to using the LaTeX package xymatrix.

Skill with LaTeX. Includes nice tables.

pgfmanual.pdf A guide to using tikz.

diagxy.pdf Documentation for a LaTeX program for drawing complicated commutative diagrams.

multicol.pdf Multiple columns in LaTeX.

PhD Graduation picture. With Eli Lebow and Johanna Franklin.