Evan Warner
Department of Mathematics, Stanford University
I
am a first-year graduate student at Stanford University,
currently supported by the
A. Craig Franklin Fellowship. My mathematical interests include number
theory (analytic and algebraic), harmonic analysis, and model theory.
I can be reached at ebwarner [at] math [dot] stanford [dot] edu or in office
380-M.
Here is a link to my CV.
Expository Notes, Articles, Links, etc.
Three approaches to Chow's
theorem (2012). Notes for a talk given to the Stanford algebraic
geometry student seminar on Chow's theorem on projective analytic varieties.
Discusses three very different proofs, due to Chow, Remmert and Stein, and
Serre.
Ultraproducts and what to do with
them (2012). Notes for a talk given to the Stanford graduate student
seminar (KIDDIE) on ultraproducts and an application to Szemerédi's
theorem.
Ultraproducts and the foundations of higher order Fourier analysis
(2012). Princeton undergraduate senior thesis, advised by Nicolas Templier.
An exposition of results of Balázs Szegedy in the field of higher
order Fourier analysis, starting from basic ultraproduct analysis and the
theory of Loeb measures.
Real analysis
qualifying exam notes (2012). Some possibly helpful notes for the
Stanford analysis qualifying exam, mostly distilled from Royden's Real
Analysis, third edition.
No guarantees either to completeness or to comprehensibility; they were
written with review in mind and would be an exceptionally poor introduction.
Notes on several complex variables: the theorems of Remmert-Stein and Chow
(2012). This and the following were presentations given, in reverse order
but not sequentially, for an undergraduate class on the theory of several
complex variables. A short presentation offering a sketch of the
Remmert-Stein theorem and Chow's theorem on projective analytic varieties.
Notes on several complex variables:
Fréchet sheaves, Cartan A and B (2012). A development of the
theory of Fréchet sheaves with application to a proof of Cartan's
Theorems A and B on Stein spaces.
Notes on several complex variables:
amalgamation of syzygies (2012). Comprising two separate lectures,
these notes carry out a proof of Cartan's Theorems A and B for simply
connected bounded polydomains, assuming only a few basic facts (notably, the
sheaf version of Hilbert's syzygy theorem and the vanishing of sheaf
cohomology for analytic sheaves on polydiscs with terminating chains of
syzygies).
Notes on several complex variables:
sheaves (2012). These notes go over some of the basic properties of
sheaves from an étalé space perspective.
Notes on modular forms: Hecke operators, oldforms and newforms (2011).
This and the following were presentations for an undergraduate seminar on
modular forms. These notes define the Hecke operators and prove a few basic
facts about them.
Notes on modular forms:
dimension formulas (2011). Using Riemann-Roch to calculate the
dimensions of the spaces of modular forms and cusp forms for important
congruence subgroups in terms of the numbers of elliptic points and cusps.
Notes on modular forms:
elliptic points and cusps (2011). A few basic facts about elliptic
points and cusps and the construction of the compactification of the modular
curve.
Siegel's theorem and its
cousins (2010). Notes written for an undergraduate seminar on elliptic
curves (two separate talks).
Nonmathematical Things
I made a crossword puzzle
recently. It should be of moderate difficulty. If you're a cheater the
solution is here.
I hope to have more (and better!) recordings at some point, but here are a
couple of piano pieces I played many years ago, in gloriously poor quality:
The g minor fugue from the Well
Tempered Clavier, Book I
The Copland passacaglia
Music I'm either currently working on or should be in my fingers somewhere:
Liszt's transcription of the Schumann lied Widmung,
Brahms' Variations on an Original Theme
Op. 21 #1, Debussy's L'isle Joyeuse,
Percy Grainger's exceptionally silly medley of British folk tunes Scotch
Strathspey and Reel, Medtner's Romantic sonata (this one's a
long-term endeavor...), the last Schubert sonata, the Beethoven "Tempest"
and "Pathetique" sonatas, Une barque sur
l'océan and Alborada del
gracioso from Ravel's Miroirs,
Scriabin's 4th sonata.
I eat at the Synergy
vegetarian cooperative. As an undergraduate, I lived at the 2
Dickinson Street cooperative at Princeton University.
I have never been known to turn down a game of Boggle or Scrabble.