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Perelman’s proof of the Poincare conjecture – a nonlinear PDE perspective		Unpublished	math.DG/0610903 Old version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	Proc. Amer. Math. Soc. 137 (2009), 2437—2440.	arXiv:0807.1900 discussion

Short stories

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	When are eigenvalues stable?
Non-measurable sets via non-standard analysis	Small samples, and the margin of error
Cohomology for dynamical systems	Infinite fields, finite fields, and the Ax-Grothendieck theorem
Sailing into the wind, or faster than the wind	The completeness and compactness theorems in first-order logic
Some notes on amenability

Open questions

• Mahler's conjecture for convex bodies

Princeton Companion to Mathematics

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

Tricks Wiki

· The tensor power trick

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
• Marker lectures (recent progress in additive prime number theory): 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, “Some topics in computational complexity”: Talk 1, Talk 2, Talk 3
• DLS: Eli Stein, “Singular integrals and several complex variables: some new perspectives”: Talk 1, Talk 2, Talk 3
• 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
• Structure and randomness: pages from year one of a mathematical blog

Back to my preprints page.