David J. Anick

David Anick, Berkeley 1980

David Jay Anick (* around 1954) is an American mathematician who studied algebra and topology .

Live and act

Anick was a Putnam Fellow in 1973 and 1975 . He graduated from the Massachusetts Institute of Technology with a bachelor's degree in 1976 and received his doctorate from Franklin Paul Peterson (A counterexample to a conjecture of Serre). He was a post-doctoral student at Stockholm University . From 1982 to 1992 he was a professor in the Faculty of Mathematics at MIT. In 1989 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ).

In his dissertation he gave a counterexample to a conjecture by Jean-Pierre Serre from the 1950s from topology (and a related conjecture from the theory of local rings). Serre assumed that the Poincaré series (power series with the rank of the rational nth homology groups as coefficients) for a loop space of a simply connected CW complex is a rational function. Anick attributed this to the construction of the Hilbert series of a finally presented Hopf algebra (with an example in which the series is irrational). A method of constructing Hopf algebras with unusual properties from algebras was introduced around the same time by Jan-Erik Roos and Clas Löfwall in Sweden (this also provided examples of irrational (transcendent) Hilbert series).

In the 1990s he switched careers and studied medicine with an MD degree in 1995 at the University of California, San Francisco , which was followed by specialist training (internship, residency) in psychiatry at McLean Hospital in Belmont . He is at the Marino Center for Integrative Health in Cambridge, Massachusetts .

In 2007 he published a paper on mathematical modeling of homeopathy .

Fonts (selection)

• Differential Algebras in Topology (= Research Notes in Mathematics. 3). AK Peters, Wellesley MA 1993, ISBN 1-56881-001-6 .
• A loop space whose homology has torsion of all orders. In: Pacific Journal of Mathematics . Vol. 123, No. 2, 1986, pp. 257-262, doi : 10.2140 / pjm.1986.123.257 .

Web links

• Homepage at the Marino Center
• Literature by and about David J. Anick in the WorldCat bibliographic database

Individual evidence

1. ↑ David J. Anick in the Mathematics Genealogy Project (English)
2. ↑ Published in Annals of Mathematics . Series 2, Volume 115, No. 1, 1982, pp. 1-33, doi : 10.2307 / 1971338 .
3. ^ MIT Faculty Mathematics
4. ^ Past Fellows. Alfred P. Sloan Foundation, accessed July 27, 2019 . 
5. ↑ Jean-Michel Lemaire: Anneaux locaux et esapces des lacets à séries de Poincaré irrationelle, d'après Anick, Roos . ( Memento of the original from October 2, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. In: Séminaire Bourbaki , No. 570, 1980/81 
6. ^ Anick: Construction d'espaces de lacets et d'anneaux locaux à séries de Poincarée-Betti non rationnelles. In: Comptes rendus des séances de l'Académie des Sciences. Series A: Sciences Mathématiques. Volume 290, No. 16, 1980, pp. 729-732 .
7. ↑ Anick: The octave potencies convention: a mathematical model of dilution and succussion. In: Homeopathy. Volume 96, No. 3, 2007, pp. 202-208, PMID 17678818 .