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Patrick Dehornoy (11 September 1952 – 4 September 2019) was a mathematician at the University of Caen who worked on set theory and algebra. He found one of the first applications of large cardinals to algebra by constructing a certain left-invariant total order, called the Dehornoy order, on the braid group. He was one of the main contributors to the development of Garside methods in group theory, leading in particular to a conjectured solution for the word problem of general Artin–Tits groups.
Dehornoy in 2013
|Died||4 September 2019(aged 66)|
|Alma mater||École Normale Supérieure|
|Institutions||University of Caen|
Education and CareerEdit
Dehornoy completed his Ph.D. in 1978 at the University of Paris, with a thesis written under the direction of Kenneth Walter McAloon. He was a Professor at the University of Caen from 1983. From 2009 to 2013, he was adjunct scientific director of the Institut national des sciences mathématiques et de leurs interactions at the CNRS.
- Dehornoy, Patrick (1994), "Braid groups and left distributive operations", Transactions of the American Mathematical Society, 345 (1): 115–150, doi:10.2307/2154598, ISSN 0002-9947, JSTOR 2154598, MR 1214782
- Dehornoy, Patrick (1995), "From large cardinals to braids via distributive algebra", Journal of Knot Theory and Its Ramifications, 4 (1): 33–79, doi:10.1142/S0218216595000041, ISSN 0218-2165, MR 1321290
- Dehornoy, Patrick; Dynnikov, Ivan; Rolfsen, Dale; Wiest, Bert (2008), Ordering braids, Mathematical Surveys and Monographs, 148, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4431-1, MR 2463428
- Dehornoy, Patrick; Digne, François; Godelle, Eddy; Krammer, Daan; Michel, Jean (2015), Foundations of Garside theory, EMS Tracts in Mathematics, 22, Zürich: European Mathematical Society, ISBN 978-3-03719-139-2, MR 3362691
- Dehornoy, Patrick (2017), "Multifraction reduction (II): conjectures for Artin–Tits groups", Journal of Combinatorial Algebra, 1 (3): 229–287, arXiv:1606.08995, doi:10.4171/JCA/1-3-1, ISSN 2415-6302, MR 3681576