This page is no longer maintained. For the updated version, see this page.

Preprints in miscellaneous topics

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Perelman’s proof of the Poincare conjecture – a nonlinear PDE perspective		Unpublished	arXiv:0610903 Old version
What is good mathematics?		Mathematical Perspectives, Bull. Amer. Math. Soc. 44 (2007), 623-634.	arXiv:0702396 Old version
Classification of almost quarter-pinched manifolds	Peter Petersen	Proc. Amer. Math. Soc. 137 (2009), 2437—2440.	arXiv:0807.1900 discussion
E pluribus unum: from complexity, universality		Daedalus, Summer 2012, 23-34 (Translated: Investigacion y Ciencia, Feb. 2015, no. 461)	web version
On the sign patterns of entrywise positivity preservers in fixed dimension	Apoorva Khare	Amer. J. Math. 143 (2021), 1863-1929. Extended abstract: FPSAC 2018, Volume 80B of Seminaire Lotharingien de Combinatoire (2018)	arXiv:1708.05197 discussion
Homogeneous length functions on groups	D.H.J. Polymath	Algebra & Number Theory 12-7 (2018), 1773--1786. DOI 10.2140/ant.2018.12.1773	arXiv:1801.03908 discussion
Commutators close to the identity		J. Op. Thy. 82:2(2019), 369–382	arXiv:1805.11131 discussion
Embedding the Heisenberg group into a bounded dimensional Euclidean space with optimal distortion		Rev. Mat. Iberoam. 37 (2021), no. 1, 1–44.	arXiv:1811.09223 discussion
A Close Call: How a Near Failure Propelled Me to Succeed		Living Proof: Stories of Resilience Along the Mathematical Journey, American Math. Society, Math. Assoc. America, 2019. A. Henderson, E. Lawrence, M. Pons, D. Taylor eds., 96--99.
Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra.	Peter Denton, Stephen Parke, Xining Zhang	Bull. Amer. Math. Soc. (N.S.) 59 (2022), no. 1, 31–58.	arXiv:1908.03795 discussion discussion II
Fractional free convolution powers. With an appendix by David Jekel	Dimitri Shlyakhtenko	To appear, Indiana U. Math. J.	arXiv:2009.01882 discussion
Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration	Asgar Jamneshan	Fundamenta Mathematicae 261 (2023), 1-98	arXiv:2010.00681 discussion
Sendov's conjecture for sufficiently high degree polynomials		Acta Mathematica, Vol. 229, No. 2 (2022), pp. 347-392	arXiv:2012.04125 discussion
The effective potential of an $M$-matrix	Marcel Filoche, Svetlana Mayboroda	J. Math. Phys. 62, 041902 (2021)	arXiv:2101.01672 discussion
Elias M. Stein (2013-2018)	Lillian Pierce et al.	Not. Amer. Math. Soc. 68 (2021), 546-563
Optimal sine and sawtooth inequalities	Louis Esser, Burt Totaro, Chengxi Wang	J. Fourier Anal. Appl. (2022) 28:14	arXiv:2107.11058 discussion
Perfectly packing a square by squares of nearly harmonic sidelength		Comp. Disc. Geom.(2023). https://doi.org/10.1007/s00454-023-00523-y	arXiv:2202.03594 discussion
Machine assisted proof		Notices Amer. Math. Soc., January 2025	pdf discussion
Mathematical exploration and discovery at scale	Bogdan Georgiev, Javier G\'omez-Serrano, Adam Zsolt Wagner		arXiv:2511.02864 discussion
Mathematical methods and human thought in the age of AI	Tanya Klowden	Submitted, Blackwell Companion to Philosophy of Math	arXiv:2603.26524 discussion
The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale	Matthew Bolan, Joachim Breitner, Jose Brox, Nicholas Carlini, Mario Carneiro, Floris van Doorn, Martin Dvorak, Andrés Goens, Aaron Hill, Harald Husum, Hernán Ibarra Mejia, Zoltan Kocsis, Bruno Le Floch, Amir Livne Bar-on, Lorenzo Luccioli, Douglas McNeil, Alex Meiburg, Pietro Monticone, Pace P. Nielsen, Emmanuel Osalotioman Osazuwa, Giovanni Paolini, Marco Petracci, Bernhard Reinke, David Renshaw, Marcus Rossel, Cody Roux, Jérémy Scanvic, Shreyas Srinivas, Anand Rao Tadipatri, Vlad Tsyrklevich, Fernando Vaquerizo-Villar, Daniel Weber, Fan Zheng	Submitted	arXiv:2512.07087 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

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

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.

This page is no longer maintained. For the updated version, see this page.

Preprints in miscellaneous topics

Papers, and projects close to completion

E pluribus unum: from complexity, universality

Daedalus, Summer 2012, 23-34

On the sign patterns of entrywise positivity preservers in fixed dimension

Amer. J. Math. 143 (2021), 1863-1929.

Homogeneous length functions on groups

D.H.J. Polymath

Algebra & Number Theory 12-7 (2018), 1773--1786. DOI 10.2140/ant.2018.12.1773

Commutators close to the identity

J. Op. Thy. 82:2(2019), 369–382

Embedding the Heisenberg group into a bounded dimensional Euclidean space with optimal distortion

Rev. Mat. Iberoam. 37 (2021), no. 1, 1–44.

A Close Call: How a Near Failure Propelled Me to Succeed

Living Proof: Stories of Resilience Along the Mathematical Journey, American Math. Society, Math. Assoc. America, 2019. A. Henderson, E. Lawrence, M. Pons, D. Taylor eds., 96--99.

Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra.

Peter Denton, Stephen Parke, Xining Zhang

Bull. Amer. Math. Soc. (N.S.) 59 (2022), no. 1, 31–58.

Fractional free convolution powers. With an appendix by David Jekel

Dimitri Shlyakhtenko

To appear, Indiana U. Math. J.

Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration

Asgar Jamneshan

Fundamenta Mathematicae 261 (2023), 1-98

Sendov's conjecture for sufficiently high degree polynomials

Acta Mathematica, Vol. 229, No. 2 (2022), pp. 347-392

The effective potential of an $M$-matrix

Marcel Filoche, Svetlana Mayboroda

J. Math. Phys. 62, 041902 (2021)

Elias M. Stein (2013-2018)

Lillian Pierce et al.

Optimal sine and sawtooth inequalities

Louis Esser, Burt Totaro, Chengxi Wang

J. Fourier Anal. Appl. (2022) 28:14

Perfectly packing a square by squares of nearly harmonic sidelength

Comp. Disc. Geom.(2023). https://doi.org/10.1007/s00454-023-00523-y

Machine assisted proof

Notices Amer. Math. Soc., January 2025

Mathematical exploration and discovery at scale

Bogdan Georgiev, Javier G\'omez-Serrano, Adam Zsolt Wagner

Mathematical methods and human thought in the age of AI

Tanya Klowden

Submitted, Blackwell Companion to Philosophy of Math

The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale

Submitted

Short stories

Open questions

Princeton Companion to Mathematics

Tricks Wiki

· The tensor power trick

Lecture Series

Presentations of talks by others

Obituaries

Miscellaneous