Daniel Litt
Stanford University Mathematics Department
Building 380, Rm. 381-M
dalitt[AT]stanford.edu
dlitt[AT]math.stanford.edu
Expository Notes and Articles
● Fulton's Trace Formula, Notes for SAGS Talk, January 23, 2012: An exposition of Fulton's trace formula in coherent cohomology, which counts the number of rational points on a projective variety over a finite field, mod p. The exposition follows Mustata and Fulton, but fills in some details.
● The Poincaré Lemma and de Rham Cohomology, The Harvard College Math Review, Vol 1. No. 2, Fall 2007: An expository account of differential forms and the Poincaré Lemma using modern methods, aimed at beginning undergraduates. Contains some minor errors and omissions (in the exterior power section), which I am attempting to get fixed in the online version.
● Introduction to Hodge-Type Structures, Harvard Undergraduate Senior Thesis, May 2010: An expository account of some Hodge Theory, concluding with a sketchy description of modern approaches (e.g. mixed Hodge modules, etc.)
● Prime Reciprocals and Primes in Arithmetic Progression, Harvard Junior Paper, May 2009: Gives some estimates on sums of prime reciprocals in certain residue classes; some of the arguments (e.g. the proofs of Propositions 5 and 6) are, to my knowledge, novel.
● Linear Independence over $Q$ and Topology, Note for MathOverflow, November 2010: Answers a MathOverflow question relating the topology of certain Riemann surfaces to the linear independence of certain numbers.
● Line Bundles on Projective Space, written for Dennis Gaitsgory's 2009-2010 Theory of Schemes course at Harvard; gives two proofs that the group of line bundles on projective space over a field is generated by the canonical bundle, and is isomorphic to the additive group of integers. That is, the only line bundles are those we know and love.
● The Hilbert Scheme of Points on a Surface, written for Dennis Gaitsgory's 2009-2010 Theory of Schemes course at Harvard; gives a very hands-off proof that the Hilbert scheme of points on a nice curve or surface is smooth and irreducible.
● A Categorical Construction of Ultrafilters, a short and extremely elementary paper written with Zachary Abel and Scott Kominers, and answering a question of E. Rosinger in the negative. To be published in the Rocky Mountain Journal of Mathematics.
● Some brief notes: A space for very short expository notes on varied subjects
Seminars
● Student Algebraic Geometry Schedule, 2012
Pictures
● Photos of Magnets, some constructions made from Zen Magnets
Non-Mathematical Writing
● "Draft Obituary, Winston Wallace 1922-2008, by Joanna Lansom," a short story I wrote in Summer 2008
● Ohio, a poem about Ohio
● The Moth at Knossos, another old poem I wrote as an exercise in mythology
● On "Old Futurism," a (mostly) silly exercise in writing a manifesto
Resumé