Francisco Santos (mathematician)

Francisco Santos Leal (born May 28, 1968 in Valladolid ) is a Spanish mathematician . He deals with discrete and combinatorial geometry, geometric and topological combinatorics, and real algebraic geometry.

Francisco Santos, Oberwolfach 2012

Life

Santos received his degree in mathematics (diploma) from the Universidad de Cantabria in Santander in 1991 (and also a degree in physics in 1996) and the Maitrise en Mathématiques Pures from the University of Grenoble I. In 1995 he received his doctorate at the Universidad de Cantabria with Tomás Recio ( Geometría Combinatoria de Curvas Algebraicas y Diagramas de Deluanay en el Plano). In 1996 he was a post-doctoral student at the University of Oxford . Since 1997 he has been adjunct professor and since 2008 full professor of geometry and topology at the Universidad de Cantabria.

In 2001 and 2007/08 he was visiting professor at the University of California, Davis , in 2003 at the MSRI and in 2008 at the École normal supérieure .

Santos refuted the long open Hirsch conjecture ( Warren M. Hirsch , 1957) for polytopes P, with n sides (dimension d-1) and dimension d:

{\ displaystyle \ delta (P) \ leq nd}

.

The diameter is defined via the associated graph of the polytope (as the maximum distance between the corners). For example, a three-dimensional cube has P n = 6, d = 3 and ${\ displaystyle \ delta (P)}$ ${\ displaystyle \ delta (P) = 3}$

In 2010 he found a counterexample with d = 38, n = 76 and diameter . He even found a family of infinitely many polytopes that violated the Hirsch conjecture (non-Hirsch polytopes), and even in every dimension. They meet , with the best value so far being (2010). ${\ displaystyle \ delta (P) = 39}$ ${\ displaystyle \ delta (P) \ sim (1+ \ epsilon) n}$ ${\ displaystyle \ epsilon = {\ frac {1} {43}}}$

The Hirsch conjecture has applications in linear optimization (especially on the question of whether the simplex algorithm is polynomial in time). The original problem was raised by Hirsch in a letter to George Dantzig in connection with the simplex method.

In 2015 he received the Fulkerson Prize for refuting the Hirsch conjecture . In 2006 he was invited speaker at the International Congress of Mathematicians in Madrid . Santos Einstein has been a visiting fellow at Freie Universität Berlin since 2016 .

Fonts

with ED Kim: An update on the Hirsch conjecture . In: Annual report of the German Mathematicians Association . Volume 112, 2010, pp. 73-98, doi : 10.1365 / s13291-010-0001-8
A counter-example to the Hirsch conjecture . In: Annals of Mathematics . Volume 176, 2012, pp. 383-412, doi : 10.4007 / annals.2012.176.1.7

Web links

Homepage

Individual evidence

↑ Francisco Santos in the Mathematics Genealogy Project (English)
↑ Francisco Santos: Geometric bistellar flips: the setting, the context and a construction (PDF; 184 kB). Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006, Volume 3, pp. 931-962.
^ Francisco Santos . In: Einstein Visiting Fellows. Einstein Foundation Berlin, accessed on May 23, 2018.

personal data
SURNAME	Santos, Francisco
ALTERNATIVE NAMES	Santos Leal, Francisco
BRIEF DESCRIPTION	Spanish mathematician
DATE OF BIRTH	May 28, 1968
PLACE OF BIRTH	Valladolid

[1] Francisco Santos in the Mathematics Genealogy Project (English)

[2] Francisco Santos: Geometric bistellar flips: the setting, the context and a construction (PDF; 184 kB). Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006, Volume 3, pp. 931-962.

[3] Francisco Santos . In: Einstein Visiting Fellows. Einstein Foundation Berlin, accessed on May 23, 2018.