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'{{Infobox scientist | name = Michel Deza | image = Michel Deza.jpg <!--(filename only, i.e. without "File:" prefix)--> | image_size = | alt = | caption = | birth_date = {{birth date and age |1939|4|27|df=y}} | birth_place = [[Moscow]], [[Soviet Union]] | death_date = <!--{{death date and age |YYYY|MM|DD |YYYY|MM|DD}} (death date then birth date)--> | death_place = | nationality = [[Russia]]n | fields = [[Mathematics]] | workplaces = | alma_mater = [[Moscow State University]] | doctoral_advisor = [[Roland Dobrushin]] <!--(or | doctoral_advisors = )--> | doctoral_students = {{plainlist|1= *[[Gérard Cohen]] *[[Monique Laurent]] }} | known_for = | awards = }} '''Michel Marie Deza''' (born 27 April 1939<ref name="preface">{{citation|title=Preface to special issue in honor of Deza's 70th birthday|url=http://www.liga.ens.fr/~deza/PrefaceYannis.pdf |first=Yannis|last=Manoussakis|journal=European Journal of Combinatorics|doi=10.1016/j.ejc.2009.03.020|year=2010|volume=31|issue=2|pages=419}}.</ref> in Moscow) is a [[USSR|Soviet]] and [[France|French]] [[mathematician]], specializing in [[combinatorics]], [[discrete geometry]] and [[graph theory]]. He is a retired director of research at the [[French National Centre for Scientific Research]] (CNRS), the vice president of the [[European Academy of Sciences]],<ref>[http://www.eurasc.org/committees/presidium.asp European Academy of Sciences Presidium], retrieved 2009-05-23.</ref> a research professor at the [[Japan Advanced Institute of Science and Technology]],<ref>[http://www.jaist.ac.jp/profiles/info_e.php?profile_id=536&syozoku=12 Faculty profile at JAIST].</ref> and one of the three founding editors-in-chief of the [[European Journal of Combinatorics]].<ref name="preface"/> Deza graduated from [[Moscow University]] in 1961, after which he worked at the [[Russian Academy of Sciences|Soviet Academy of Sciences]] until emigrating to France in 1972.<ref name="preface"/> In France, he worked at CNRS from 1973 until his 2005 retirement.<ref name="preface"/> He has written eight books and about 270 academic papers with 75 different co-authors and co-editors,<ref name="preface"/> including four papers with [[Paul Erdős]], giving him an [[Erdős number]] of 1.<ref>[https://files.oakland.edu/users/grossman/enp/Erdos0d.html Erdos0d, Version 2007, September 3, 2008], from the Erdős number project.</ref> The papers from a conference on combinatorics, geometry and computer science, held in Luminy, France in May 2007, have been collected as a special issue of the European Journal of Combinatorics in honor of Deza's 70th birthday.<ref name="preface"/> ==Selected papers== *{{citation|year=1974|title=Solution d'un problème de Erdös-Lovász|first=M.|last=Deza|journal=Journal of Combinatorial Theory, Series B|volume=16|issue=2|pages=166–167|doi=10.1016/0095-8956(74)90059-8|mr=0337635}}. This paper solved a [[Erdős conjecture|conjecture]] of [[Paul Erdős]] and [[László Lovász]] (in [http://www.math-inst.hu/~p_erdos/1975-32.pdf], p.&nbsp;406) that a sufficiently large family of ''k''-subsets of any ''n''-element universe, in which the intersection of every pair of ''k''-subsets has exactly ''t'' elements, has a common ''t''-element set shared by all the members of the family. Manoussakis<ref name="preface"/> writes that Deza is sorry not to have kept and framed the US$100 check from Erdős for the prize for solving the problem, and that this result inspired Deza to pursue a lifestyle of mathematics and travel similar to that of Erdős. *{{citation|year=1983|title=On functions of strength ''t''|first1=M.|last1=Deza|first2=P.|last2=Frankl|author2-link=Péter Frankl|first3=N. M.|last3=Singhi|author3-link=Navin M. Singhi|journal=[[Combinatorica]]|volume=3|issue=3–4|pages=331–339|doi=10.1007/BF02579189|mr=0729786}}. This paper considers functions ƒ from subsets of some ''n''-element universe to integers, with the property that, when ''A'' is a small set, the sum of the function values of the supersets of ''A'' is zero. The strength of the function is the maximum value ''t'' such that all sets ''A'' of ''t'' or fewer elements have this property. If a [[family of sets]] ''F'' has the property that it contains all the sets that have nonzero values for some function ƒ of strength at most ''t'', ''F'' is ''t''-dependent; the ''t''-dependent families form the dependent sets of a [[matroid]], which Deza and his co-authors investigate. *{{citation|year=1992|title=Facets for the cut cone I|first1=M.|last1=Deza|first2=M.|last2=Laurent|journal=Mathematical Programming|volume=56|issue=1–3|pages=121–160|doi=10.1007/BF01580897|mr=1183645}}. This paper in [[polyhedral combinatorics]] describes some of the facets of a [[polytope]] that encodes cuts in a [[complete graph]]. As the [[maximum cut]] problem is [[NP-complete]], but could be solved by [[linear programming]] given a complete description of this polytope's facets, such a complete description is unlikely. *{{citation|year=1996|contribution=On skeletons, diameters and volumes of metric polyhedra|first1=A.|last1=Deza|first2=M.|last2=Deza|first3=K.|last3=Fukuda|title=Combinatorics and Computer Science|series=Lecture Notes in Computer Science|volume=1120|publisher=Springer-Verlag|pages=112–128|doi=10.1007/3-540-61576-8_78|url=http://www.cas.mcmaster.ca/~deza/lncs1996.pdf|mr=1448925}}. This paper with Antoine Deza, who holds a [[Canada Research Chair]] in Combinatorial Optimization at [[McMaster University]], combines Michel Deza's interests in polyhedral combinatorics and metric spaces; it describes the metric polytope, whose points represent symmetric distance matrices satisfying the triangle inequality. For metric spaces with seven points, for instance, this polytope has 21 dimensions (the 21 pairwise distances between the points) and 275,840 vertices. *{{citation|year=1997|title=Clin d'oeil on ''L''₁-embeddable planar graphs|first1=V.|last1=Chepoi|first2=M.|last2=Deza|first3=V.|last3=Grishukhin|journal=Discrete Applied Mathematics|volume=80|issue=1|pages=3–19|doi=10.1016/S0166-218X(97)00066-8|mr=1489057}}. Much of Deza's work concerns [[Isometry|isometric]] embeddings of graphs (with their [[shortest path]] metric) and metric spaces into vector spaces with the ''L''₁ distance; this paper is one of many in this line of research. An earlier result of Deza showed that every ''L''₁ metric with rational distances could be scaled by an integer and embedded into a [[hypercube]]; this paper shows that for the metrics coming from [[planar graph]]s (including many graphs arising in [[chemical graph theory]]), the scale factor can always be taken to be&nbsp;2. ==Books== *{{citation|last1=Deza|first1=M.|first2=M.|last2=Laurent|title=Geometry of cuts and metrics|series=Algorithms and Combinatorics|volume=15|year=1997|publisher=Springer|isbn=3-540-61611-X|mr=1460488}}. As [[MathSciNet]] reviewer [[Alexander Barvinok]] writes, this book describes "many interesting connections ... among polyhedral combinatorics, local Banach geometry, optimization, graph theory, geometry of numbers, and probability". *{{citation|last1=Deza|first1=M.|first2=V.|last2=Grishukhin|first3=M.|last3=Shtogrin|title=Scale-isometric polytopal graphs in hypercubes and cubic lattices|url=http://www.worldscibooks.com/mathematics/p308.html|year=2004|publisher=Imperial College Press|isbn=1-86094-421-3|mr=2051396}}. A sequel to ''Geometry of cuts and metrics'', this book concentrates more specifically on ''L''₁ metrics. *{{citation|last1=Deza|first1=E.|first2=M.|last2=Deza|title=Dictionary of Distances|year=2006|publisher=Elsevier|isbn=0-444-52087-2}}. Reviewed in [http://www.scribd.com/doc/2668595/Newsletter-of-the-European-Mathematical-Society-20070664-featuring-Let-Platonism-Die ''Newsletter of the European Mathematical Society'' '''64''' (June 2007)], p.&nbsp;57. This book is organized as a list of distances of many types, each with a brief description. *{{citation|first=M.|last=Deza|first2=M. |last2=Dutour Sikirić|title=Geometry of chemical graphs: polycycles and two-faced maps|series=Encyclopedia of Mathematics and its Applications|volume=119|year=2008|publisher=Cambridge University Press|isbn=978-0-521-87307-9|mr=2429120}}. This book describes the graph-theoretic and geometric properties of [[fullerene]]s and their generalizations, planar graphs in which all faces are cycles with only two possible lengths. *{{citation|first1=M.|last1=Deza|first2=E.|last2=Deza|title=Encyclopedia of Distances|year=2009|publisher=Springer-Verlag|isbn=978-3-642-00233-5}}, *{{citation|first1=E.|last1=Deza|first2=M.|last2=Deza|title=Figurate Numbers|year=2011|publisher=World Scientific|isbn=978-981-4355-48-3}}. *{{citation|first1=M.|last1=Deza|first2=E.|last2=Deza|title=Encyclopedia of Distances, 2nd revised edition|year=2013|publisher=Springer-Verlag|isbn=978-3-642-30957-1}}. *{{citation|first1=M.|last1=Deza|first2=E.|last2=Deza|title=Encyclopedia of Distances, 3rd revised edition|year=2014|publisher=Springer-Verlag|isbn=978-3-662-44341-5}}. *{{citation|first1=M.|last1=Deza|first2=E.|last2=Deza|title=Encyclopedia of Distances, 4th revised edition|year=2016|publisher=Springer-Verlag|isbn=978-3-662-52844-0}}. *{{citation|last1=Deza|first1=M.|first2=M.|last2=Dutour Sikirić|first3=M.|last3=Shtogrin|title=Geometric Structure of Chemistry-relevant Graphs|year=2015|publisher=Springer|isbn=978-81-322-2448-8}}. *{{citation|last1=Deza|first1=E.|first2=M.|last2=Deza|first3=M.|last3=Dutour Sikirić|title=Generalizations of Finite Metrics and Cuts|year=2016|publisher=World Scientific|isbn=978-98-147-4039-5}}. ==Poetry in Russian== *Deza, M. (1983), ''59--62,'' Sintaksis, Paris (<nowiki>http://dc.lib.unc.edu/cdm/item/collection/rbr/?id=30912</nowiki>). *{{citation|first1=M.|last1=Deza|title=Poems and interviews|year=2014|publisher=Probel-2000, Moscow|isbn=978-5-98604-442-2}} (http://www.liga.ens.fr/~deza/InRussian/DEZA-M.pdf). *{{citation|first1=M.|last1=Deza|title=75--77|year=2016|publisher=Probel-2000, Moscow|isbn=978-5-98604-555-9}} (http://www.liga.ens.fr/~deza/InRussian/DEZA-M2.pdf). ==References== {{reflist}} ==External links== *[http://www.liga.ens.fr/~deza/ Deza's web page] {{Authority control}} {{DEFAULTSORT:Deza, Michel}} [[Category:1939 births]] [[Category:Living people]] [[Category:Russian mathematicians]] [[Category:Combinatorialists]] [[Category:Graph theorists]] [[Category:20th-century French mathematicians]] [[Category:21st-century French mathematicians]] [[Category:Academic journal editors]] [[Category:Soviet emigrants to France]]'