Preprints in miscellaneous topics

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Papers, and projects close to completion

Title	With	Status	Download
On the Structure of Projective Group Representations in Quaternionic Hilbert Space	Andrew Millard	J. Math. Phys. 37 (1996), 5848-5857	dvi
Relative efficiencies of kernel and local likelihood density estimators	Peter Hall	J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002), 537-547	dvi
Perelman’s proof of the Poincare conjecture – a nonlinear PDE perspective		Unpublished	math.DG/0610903 Old version
What is good mathematics?		Mathematical Perspectives, Bull. Amer. Math. Soc. 44 (2007), 623-634.	math.HO/0702396 Old version
Classification of almost quarter-pinched manifolds	Peter Petersen	Submitted, Proc. Amer. Math. Soc.	arXiv:0807.1900 discussion

Short stories

These are generally very short, toy versions of real results due to other people, and are not publication-quality.  Caveat emptor.  All files other than figures are in dvi format.  Unlike the preprints, these articles are fluid and subject to new developments.  Please let me know if you have any comments, references, etc. on any of them.

Disclaimer: Many of the notes here are based on papers written by other people.  My intention here is not to try to "beat" these authors' work in any way, but rather to isolate the main ingredients of the argument, which are often very beautiful, and try to present them in as simple and brief a context as possible (often sacrificing generality, rigour, and/or details in order to do this).  Certainly I do not view these notes as worthy of publication in a refereed journal, and are definitely inferior to the original article in every single aspect, with the possible exception of brevity.
 

Notes on discrete Black-Scholes theory	Arrow's theorem
The Lagarias-Shor tiling of R^{12}	A lemma of Beck
On a problem by Arens, Goldberg, and Luxemburg (with Raymond Redheffer)	The Skolem-Mahler-Lech theorem [discussion]
Quantitative spectral theory of compact operators	The Banach-Tarski paradox
The Baker-Campbell-Hausdorff formula	Quasi-metric spaces
Squares, cubes, and smooth functions	Quantum mechanics and Tomb Raider
Dyadic models	The Chayes-McKellar-Winn theorem
Non-firstorderisability	Pythagoras' theorem
The Hahn-Banach theorem, Menger's theorem, and Helly's theorem	Hilbert's nullstellensatz
Einstein's derivation of E=mc^2	The strong law of large numbers
The Black-Scholes equation

Open questions

• Mahler's conjecture for convex bodies
  

Princeton Companion to Mathematics

• Compactness and compactification [discussion]
• Differential forms and integration [discussion]
• Ricci flow [discussion]
  

Lecture Series

• Simons lectures (the dichotomy between structure and randomness): Talk 1, Talk 2, Talk 3
• Milliman lectures (recent progress in arithmetic combinatorics): Talk 1, Talk 2, Talk 3
• Lewis lectures (The regularity lemma, and random matrices): Talk 1, Talk 2, Talk 3, Talk 4
  

Presentations of talks by others

• 2006 ICM: Étienne Ghys, “Knots and dynamics”
• Fields Medalist Symposium
  
• DLS: Shou-wu Zhang, "Rational Points on Curves": Talk 1, Talk 2, Talk 3
  
• DLS: Shing-Tung Yau, "Geometric Structures on Manifolds": Talk 1, Talk 2, Talk 3
• DLS: Charlie Fefferman, "Interpolation of functions on R^n": Talk 1, Talk 2, Talk 3
• DLS: Avi Wigderson,
  
• Rosemary Grant, "Darwin’s finches and introgressive hybridisation"

Obituaries

• Paul Cohen
• Atle Selberg
  

Miscellaneous

• Does P = NP? + Figure.  This is a 10-minute talk given at the UNSW high school math competition prize ceremony.  Appears in Parabola 36 (2000) No. 3, 2-7.
• The cosmic distance ladder.  This is a talk aimed at high school math teachers. (2006)  Video available here. [discussion]
  
• Vitae
• Thesis home page.  My thesis, "Three regularity results in harmonic analysis", has appeared in "Topics in Analysis and Applications", World Scientific.
• Java applets

Back to my preprints page.