AlexanderGrothendiecksMathematicalGenealogy 2010-05-09 17:38:43 2010-05-09 17:38:43 Biography mathematical `genealogy' Alexander Grothendieck % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \usepackage{amsmath, amssymb, amsfonts, amsthm, amscd, latexsym} \usepackage{xypic} \usepackage[mathscr]{eucal} \theoremstyle{plain} \newtheorem{lemma}{Lemma}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}{Corollary}[section] \theoremstyle{definition} \newtheorem{definition}{Definition}[section] \newtheorem{example}{Example}[section] %\theoremstyle{remark} \newtheorem{remark}{Remark}[section] \newtheorem*{notation}{Notation} \newtheorem*{claim}{Claim} \renewcommand{\thefootnote}{\ensuremath{\fnsymbol{footnote%%@ }}} \numberwithin{equation}{section} \newcommand{\Ad}{{\rm Ad}} \newcommand{\Aut}{{\rm Aut}} \newcommand{\Cl}{{\rm Cl}} \newcommand{\Co}{{\rm Co}} \newcommand{\DES}{{\rm DES}} \newcommand{\Diff}{{\rm Diff}} \newcommand{\Dom}{{\rm Dom}} \newcommand{\Hol}{{\rm Hol}} \newcommand{\Mon}{{\rm Mon}} \newcommand{\Hom}{{\rm Hom}} \newcommand{\Ker}{{\rm Ker}} \newcommand{\Ind}{{\rm Ind}} \newcommand{\IM}{{\rm Im}} \newcommand{\Is}{{\rm Is}} \newcommand{\ID}{{\rm id}} \newcommand{\GL}{{\rm GL}} \newcommand{\Iso}{{\rm Iso}} \newcommand{\Sem}{{\rm Sem}} \newcommand{\St}{{\rm St}} \newcommand{\Sym}{{\rm Sym}} \newcommand{\SU}{{\rm SU}} \newcommand{\Tor}{{\rm Tor}} \newcommand{\U}{{\rm U}} \newcommand{\A}{\mathcal A} \newcommand{\Ce}{\mathcal C} \newcommand{\D}{\mathcal D} \newcommand{\E}{\mathcal E} \newcommand{\F}{\mathcal F} \newcommand{\G}{\mathcal G} \newcommand{\Q}{\mathcal Q} \newcommand{\R}{\mathcal R} \newcommand{\cS}{\mathcal S} \newcommand{\cU}{\mathcal U} \newcommand{\W}{\mathcal W} \newcommand{\bA}{\mathbb{A}} \newcommand{\bB}{\mathbb{B}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bD}{\mathbb{D}} \newcommand{\bE}{\mathbb{E}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bG}{\mathbb{G}} \newcommand{\bK}{\mathbb{K}} \newcommand{\bM}{\mathbb{M}} \newcommand{\bN}{\mathbb{N}} \newcommand{\bO}{\mathbb{O}} \newcommand{\bP}{\mathbb{P}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bV}{\mathbb{V}} \newcommand{\bZ}{\mathbb{Z}} \newcommand{\bfE}{\mathbf{E}} \newcommand{\bfX}{\mathbf{X}} \newcommand{\bfY}{\mathbf{Y}} \newcommand{\bfZ}{\mathbf{Z}} \renewcommand{\O}{\Omega} \renewcommand{\o}{\omega} \newcommand{\vp}{\varphi} \newcommand{\vep}{\varepsilon} \newcommand{\diag}{{\rm diag}} \newcommand{\grp}{{\mathbb G}} \newcommand{\dgrp}{{\mathbb D}} \newcommand{\desp}{{\mathbb D^{\rm{es}}}} \newcommand{\Geod}{{\rm Geod}} \newcommand{\geod}{{\rm geod}} \newcommand{\hgr}{{\mathbb H}} \newcommand{\mgr}{{\mathbb M}} \newcommand{\ob}{{\rm Ob}} \newcommand{\obg}{{\rm Ob(\mathbb G)}} \newcommand{\obgp}{{\rm Ob(\mathbb G')}} \newcommand{\obh}{{\rm Ob(\mathbb H)}} \newcommand{\Osmooth}{{\Omega^{\infty}(X,*)}} \newcommand{\ghomotop}{{\rho_2^{\square}}} \newcommand{\gcalp}{{\mathbb G(\mathcal P)}} \newcommand{\rf}{{R_{\mathcal F}}} \newcommand{\glob}{{\rm glob}} \newcommand{\loc}{{\rm loc}} \newcommand{\TOP}{{\rm TOP}} \newcommand{\wti}{\widetilde} \newcommand{\what}{\widehat} \renewcommand{\a}{\alpha} \newcommand{\be}{\beta} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\de}{\delta} \newcommand{\del}{\partial} \newcommand{\ka}{\kappa} \newcommand{\si}{\sigma} \newcommand{\ta}{\tau} \newcommand{\lra}{{\longrightarrow}} \newcommand{\ra}{{\rightarrow}} \newcommand{\rat}{{\rightarrowtail}} \newcommand{\oset}[1]{\overset {#1}{\ra}} \newcommand{\osetl}[1]{\overset {#1}{\lra}} \newcommand{\hr}{{\hookrightarrow}} \section{Alexander Grothendieck} (n\'ee `` Alexander Raddatz '' in Berlin, Germany; French adopted name: Alexandre Grothendieck, with the last name being his mother's maiden name.) \bigbreak \subsection{Mathematical `Genealogy'} %%%%%%%%%%%%% Ph.D. Universit\'e Henri Poincar\'e Nancy 1 \\ Dissertation: ``Produits tensoriels topologiques et \'espaces nucl\'eaires.'' \\ Mathematics Subject Classification: 14 = Algebraic Geometry \\ Advisor No. 1: Laurent Schwartz \\ Advisor No. 2: Jean Dieudonn\'e \\ \subsection{Alexander Grothendieck's Students' List:} (incomplete)\\ Name--- School--- Year --- --------Descendants----- \\ Pierre Berthelot 1 \\ Carlos Contou-Carrère Université Montpellier II 1983 2 \\ {\em Pierre Deligne} Université Libre de Bruxelles 1968 62 \\ Michel Demazure Université de Paris 1965 15 \\ Luc Illusie 1971 22 \\ Yves Ladegaillerie Université Montpellier II 1976 \\ William Messing Princeton University 1971 5 \\ Michel Raynaud 7 \\ Hoang Sinh Université Denis Diderot - Paris VII 1975 \\ Jean-Louis Verdier 1967 28 %%%%%%%%%% \bigbreak \textbf{Alexander Grothendieck's Doctoral Advisor No.1--Laurent Schwartz: \\ A Concise Biography and `Genealogy':}\\ %%%%%%%% Ph.D. Université Louis Pasteur-- Strasbourg I 1943 \\ Dissertation: ``Sommes de Fonctions Exponentielles R\'eelles'' \\ Advisor: {\em Georges Valiron} \\ \subsection{Student(s):} \bigbreak \med Table \\ Name--- School--- Year-------- Descendants \\ Bernard Beauzamy Université Denis Diderot - Paris VII 1976 25 \\ Louis Boutet de Monvel 34 \\ Georges Glaeser Université Henri Poincaré Nancy 1 1957 3 \\ {\bf Alexander Grothendieck} Université Henri Poincaré Nancy 1 152 \\ Jacques-Louis Lions Université Henri Poincaré Nancy 1 1954 1,202 \\ Bernard Malgrange Université Henri Poincaré Nancy 1 1955 21 \\ André Martineau 37 \\ Bernard Maurey Université Denis Diderot - Paris VII 1973 4 \\ M. Narasimhan \\ Gilles Pisier Université Denis Diderot - Paris VII 1977 23 \\ Erik Thomas 14 \\ J. François Treves Université Paris IV-Sorbonne 34 \\ Andre Unterberger Université Denis Diderot - Paris VII 1 \\ Ali Ustunel Université Paris VI - Pierre et Marie Curie 1981 4 \\ \med {\em Note:} According to the on-line databases, Laurent Schwartz has 14 students and 1,544 descendants.\\ Laurent Schwartz \\ (1915 - 2002)\\ List of References (5 books/articles) \\ {\bf Honours awarded to Laurent Schwartz} \\ Speaker at International Congress 1950 \\ Fields Medal 1950 \\ British Mathematical Colloquium plenary speaker 1954 . \\ References for Laurent Schwartz\\ -------------------------------------------- Obituary in The Times [available on the Web] \\ \subsection{Articles:} \bigbreak H. Bohr, The work of L. Schwartz, Proceedings of the International Congress of Mathematicians, Harvard, 1950 (Providence, RI, 1952). \\ B. L. Malgrange, Schwartz et la th\'eorie des distributions, in Colloquium in honor of Laurent Schwartz 1 (Palaiseau, 1983), Astérisque No. 131 (1985), 25-33. \\ L. Schwartz, Notice sur les travaux scientifiques de Laurent Schwartz, in Mathematical analysis and applications A (New York-London, 1981), 1-25. \\ L. Schwartz, Calcul infinit\'esimal stochastique, in Analyse Math\'ematique et Applications (1988). \\ Source: Encyclopaedia Britannica. $$<a href="http://www.genealogy.math.ndsu.nodak.edu">$$ $$<img src="http://www.genealogy.math.ndsu.nodak.edu/img/treebutton.gif"$$ $$width="80" height="86" alt="The Mathematics Genealogy Project"$$ $$style="border: 0" /></a>$$