The braid group order introduced by Patrick Dehornoy bridged the gap between large cardinals and algebra, providing a novel way to structure mathematical objects. As a French mathematician primarily associated with the University of Caen Normandy, his work fundamentally altered the understanding of braid groups and left-invariant orderings throughout his long career in set theory.
Academic Background
Born in Rouen on 11 September 1952, Dehornoy completed his secondary education at Lycée Pierre-Corneille in 1971. He proceeded to the École Normale Supérieure from 1971 to 1975 before moving to the University of Paris. Under the supervision of Kenneth Walter McAloon, he completed his Ph.D. in 1978. His early professional research occurred at the French National Centre for Scientific Research between 1975 and 1982.
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In 1983, Dehornoy began his tenure at the University of Caen Normandy. He served as a professor there until 2017, after which he maintained an emeritus status until his death in 2019. Beyond his university duties, he served as an adjunct scientific director for the Institut national des sciences mathématiques et de leurs interactions at the CNRS from 2009 to 2013.
Contributions to Group Theory
His primary mathematical legacy involves the application of large cardinals to algebraic structures. He successfully constructed the Dehornoy order, a left-invariant total order on the braid group. Later, he focused on Garside methods and developed efficient algorithms for comparing braids. His book, Foundations of Garside Theory, earned him the EMS Monograph Award in 2014.
Awards and Recognition
The mathematical community recognized his output with several honors. He received the Ferran Sunyer i Balaguer Prize in 1998 and the Prix Langevin from the French Academy of Sciences in 2005. Furthermore, he was appointed a senior member of the Institut Universitaire de France in 2002, with a subsequent renewal in 2007.
Fast facts
- Born: 11 September 1952, Rouen, France
- Died: 4 September 2019, Villejuif, France
- Field: Set theory and algebra
- Key achievement: Dehornoy order on braid groups
- PhD Advisor: Kenneth Walter McAloon
- Award: Ferran Sunyer i Balaguer Prize (1998)
- Award: Langevin prize (2005)
- Membership: Institut Universitaire de France
Questions readers ask
What is the Dehornoy order?
It is a specific left-invariant total order on the braid group, representing an application of large cardinal theory to algebra.
Where did Patrick Dehornoy spend most of his career?
He was a professor at the University of Caen Normandy from 1983 until his transition to emeritus status in 2017.
Achievements
- Langevin prize — 2005
- Ferran Sunyer i Balaguer Prize — 1998
- Held posts at University of Caen Normandy
- Fields: mathematics and set theory
