**Francisco (Paco) Santos Leal** (born May 28, 1968) is a Spanish mathematician at the University of Cantabria, known for finding a counterexample to the Hirsch conjecture in polyhedral combinatorics.^{ [1] }^{ [2] }^{ [3] } In 2015 he won the Fulkerson Prize for this research.^{ [4] }

Santos was born in Valladolid, Spain.^{ [5] } He earned a licenciate in mathematics from the University of Cantabria in 1991, and a master's degree in pure mathematics from Joseph Fourier University in Grenoble, France in the same year.^{ [5] } He returned to Cantabria for his doctorate, which he finished in 1995, with a thesis on the combinatorial geometry of algebraic curves and Delaunay triangulations supervised by Tomás Recio.^{ [6] } He also has a second licenciate, in physics, from Cantabria in 1996. After postdoctoral studies at the University of Oxford he returned to Cantabria as a faculty member in 1997, and was promoted to full professor in 2008. From 2009 to 2013 he has been vice-dean of the Faculty of Sciences at Cantabria.^{ [5] }

As well as being honored by the Fulkerson Prize in 2015 for a counter-example of the Hirsch conjecture,^{ [1] }^{ [4] } he was an invited sectional speaker at the 2006 International Congress of Mathematicians.^{ [5] }

Santos is an Editor-in-Chief of the Electronic Journal of Combinatorics.^{ [7] }

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In mathematical programming and polyhedral combinatorics, the **Hirsch conjecture** is the statement that the edge-vertex graph of an *n*-facet polytope in *d*-dimensional Euclidean space has diameter no more than *n* − *d*. That is, any two vertices of the polytope must be connected to each other by a path of length at most *n* − *d*. The conjecture was first put forth in a letter by Warren M. Hirsch to George B. Dantzig in 1957 and was motivated by the analysis of the simplex method in linear programming, as the diameter of a polytope provides a lower bound on the number of steps needed by the simplex method. The conjecture is now known to be false in general.

**Polyhedral combinatorics** is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

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**Geordie Williamson** is an Australian mathematician at the University of Sydney. He became the youngest living Fellow of the Royal Society when he was elected in 2018 at the age of 36.

- 1 2 Santos, Francisco (2011), "A counterexample to the Hirsch conjecture",
*Annals of Mathematics*,**176**(1): 383–412, arXiv: 1006.2814 , doi:10.4007/annals.2012.176.1.7, MR 2925387, S2CID 15325169 - ↑ "Francisco Santos encuentra un contraejemplo que refuta la conjetura de Hirsch",
*Gaussianos*, May 24, 2010 - ↑ Kalai, Gil (10 May 2010), "Francisco Santos Disproves the Hirsch Conjecture",
*Combinatorics and more*, retrieved 2015-07-18. - 1 2 2015 Fulkerson Prize citation, retrieved 2015-07-18.
- 1 2 3 4 Curriculum vitae Archived 2016-04-16 at the Wayback Machine , retrieved 2015-07-18.
- ↑ Francisco Santos Leal at the Mathematics Genealogy Project
- ↑ "Editorial Team, Electronic Journal of Combinatorics" . Retrieved 24 July 2015.

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