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	Jacques Tits - Wikipedia, the free encyclopedia
		Jacques Tits (born August 12, 1930) is a French mathematician, formerly Belgian.
		The related theory of (B,N) pairs is a basic tool in the theory of groups of Lie type.
		Tits received the Wolf Prize in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction " Pour le Mérite".
	en.wikipedia.org /wiki/Jacques_Tits (211 words)

	Tit - Unipedia (Site not responding. Last check: 2007-10-08)
		Tit, a variant of teat, is a slang (one of the seven dirty words) term for breast or nipple.
		TiT can also refer to a "Tranceaddict in Training", or someone who is most likely going to ask about Tiesto, how to download Trance music MP3's, or spam free I-Pods.
		Tit is also used in the name of the strategy called Tit for Tat.
	www.unipedia.info /Tit.html (301 words)

	Math 757 Announcement (Site not responding. Last check: 2007-10-08)
		Buildings are simplicial complexes that were introduced by Jacques Tits in an attempt to give a unified geometric interpretation of the simple Lie groups, especially the exceptional ones.
		Jacques Tits, Buildings of spherical type and finite BN-pairs, Springer-Verlag, Berlin, 1974, Lecture Notes in Mathematics, Vol.
		Jacques Tits, Twin buildings and groups of Kac-Moody type, Groups, combinatorics and geometry (Durham, 1990), Cambridge Univ. Press, Cambridge, 1992, pp.
	www.math.cornell.edu /~kbrown/757/announcement.html (234 words)

	Lacanian Press Agency
		Bouveresse answers from his Chair, that his own position still requires working through, on the basis of his "strong sense of psychic reality" and his refusal to admit that "mathematical structures are the only things that end up being real".
		Tits mentions several rather extreme and less consensual cases in which it becomes hard for a mathematician to account on the flboard for the validity of a theorem.
		This may happen because the proof is exorbitant (several thousand pages for the classification of simple finite groups), or it requires colossal culture (Fermat's Great Theorem), or it may rest on finite yet inhuman combinatorial verifications readily performed by a computer (the four-colour theorem).
	www.lacan.com /agenceo24e.html (2116 words)

	Lectures and Colloquia (Site not responding. Last check: 2007-10-08)
		This is a beautiful example of a theorem in which a few purely geometrical hypotheses end up implying that the only examples display a high degree of symmetry.
		Since the class of generalized polygons include the incidence graphs of arbitrary projective planes and these are too numerous to classify, it is not possible to extend Tits' result to arbitrary spherical buildings of rank two.
		In recent work, however, Tits and the speaker have succeeded in extending Tits' original theorem under the so-called Moufang condition.
	www.inf.fu-berlin.de /graduate-programs/cgc/Veranstaltungen/Vorlesungen/SS04/vl-7.6.html (269 words)

	Armand Borel bei eLexi - das Onlinelexikon (Site not responding. Last check: 2007-10-08)
		He was in Paris from 1949: he applied the Leray spectral sequence to the topology of Lie groups and their classifying spaces, under the influence of Leray and Henri Cartan.
		He collaborated with Jacques Tits in fundamental work on algebraic groups, and with Harish-Chandra on their arithmetic subgroups.
		In an algebraic group G a Borel subgroup H is one such that the homogeneous space G/H is a projective variety, and as small as possible.
	www.elexi.de /en/a/ar/armand_borel.html (487 words)

	Peter Abramenko, Abstract (Site not responding. Last check: 2007-10-08)
		They were introduced and classified (for irreducible rank greater than 2) by Jacques Tits.
		The corresponding geometric objects are twin buildings, which were introduced in the late 1980's by Ronan and Tits and generalize spherical buildings.
		In the talk, some group theoretic results (presentations; homological finiteness properties) will be discussed which heavily rely on the geometry/topology of the (twin) buildings these groups are acting on.
	www.math.binghamton.edu /dept/topsem/00Abstracts/pa2000.html (137 words)

	[No title]
		The complex Lie group E_6 acts on the 'complexified Cayley plane' where you replace the Cayley algebra O by O tensor C. You obtain a so-called V-plane (formerly known as Hjelmslev plane).
		Tits invented them in order to produce nice geometries for all exeptional groups.
		Tits' lecture note 'Buildings of spherical type and finite BN pairs' is a great reference.
	www.math.niu.edu /~rusin/known-math/00_incoming/projplane (3734 words)

	Weiss, R.M.: The Structure of Spherical Buildings.
		Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property.
		Moufang buildings of rank two were recently classified by Tits and Weiss.
		He is the coauthor, with Jacques Tits, of Moufang Polygons.
	www.pupress.princeton.edu /titles/7794.html (357 words)

	Coxeter Groups II
		In some circumstances, for example in low-dimensional graphics or investigating the geometry of regions of the Tits cone, this is a reasonable choice, but usually it is a very poor one.
		To avoid round-off errors (a potentially serious problem), it is a good idea to use a Cartan matrix with integral coordinates if it exists (as it does for the crystallographic groups), or the standard realization, in which case you are faced with arithmetic in cyclotomic fields.
		Nonetheless, Tits' reductions are easy enough to carry out by hand in simple cases, and his Theorem assures that this effort will not be fruitless.
	www.math.ubc.ca /~cass/coxeter/crm2.html (4798 words)

	Bibliography
		Jacques Tits, Le plan projectif des octaves et les groupes de Lie exceptionnels, Bull.
		Jacques Tits, Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionnelles, Indag.
		Jacques Tits, Buildings of Spherical Type and Finite BN-Pairs, Lecture Notes in Mathematics, Vol.
	math.ucr.edu /home/baez/octonions/node22.html (1218 words)

	Weiss, R.M.: Quadrangular Algebras. (MN-46).
		Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras.
		Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring.
		He is the author of The Structure of Spherical Buildings (Princeton) and the coauthor (with Jacques Tits) of Moufang Polygons.
	pup.princeton.edu /titles/8116.html (276 words)

	Gromov: Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
		Gromov: Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
		Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits).
		TITS, Free subgroups in linear groups, J. Algebra, 20 (
	www.numdam.org /item?id=PMIHES_1981__53__53_0 (96 words)

	Summer School on Finite Group Theory (Site not responding. Last check: 2007-10-08)
		These are the buildings whose apartments have a natural representation as a tiling of a Euclidean space: We will study sectors, the building at infinity (which is spherical) and root data with valuation.
		Two of Jacques Tits' most remarkable accomplishments are his classification of spherical buildings and his classification (some of it in collaboration with F. Bruhat) of affine buildings (in sufficiently high rank).
		One goal of this course is to leave the students with some understanding of these two results.
	www.dimi.uniud.it /mainards/scuolaestiva2005/Weiss.htm (221 words)

	Jacques Treatment: NerdGod?
		NerdGod II Jacques strapped for words to praise Da daa Kooning a moment before boarding Trans-Vestite Air Line flight Zero (Study)
		Jacques strapped for words to praise Da daa Kooning a moment before boarding Trans-Vestite Air Line flight Zero (Final)
		Jacques Learns the Hula, Version 2 (The Full Montie)
	www.treatmentlabs.com /nerd_god.html (200 words)

	I just bought a harpsichord! - @forums (Site not responding. Last check: 2007-10-08)
		And I won't even begin to tell you about Caught a Lite Sneeze and Blood Roses....
		Send a private message to Tits of Clay
		I didn't know that a harpsichord had a dual keyboard.
	www.atforumz.com /showthread.php?t=218684 (357 words)

	[No title]
		Hans Freudenthal, Lie groups in the foundations of geometry, Adv.
		18) Jacques Tits, Le plan projectif des octaves et les groupes de Lie exceptionnels, Bull.
		Jacques Tits, Le plan projectif des octaves et les groupes exceptionnels E_6 et E_7, Bull.
	www.math.niu.edu /~rusin/known-math/00_incoming/jordanalg (2936 words)

	HogBlog: Mathematics Archives
		If you run a Google search on Tits Group, your first hit will be an entry at Mathworld.
		I believe this group to be named after Jacques Tits, a Belgian mathematician who should never, ever have his own web page.
		If one were to write a book about Jacques Tits' influence on module theory, one could call it Tits and Ass.
	www.koschei.net /blog/archives/cat_mathematics.html (11705 words)

	Walter Feit. In Memoriam
		Of course Walter counted among his friends Brauer and Thompson and Serre and Tits and Steinberg..
		He exuded this sense of mathematics as a delightful conversation across the centuries.
		Last year when Len Scott and I organized a conference here for Walter, I was moved by the responses to my invitation from my heroes of his generation..
	www.math.yale.edu /public_html/WalterFeit/Speakers/Solomon.html (718 words)

	Washingtonpost.com: Live Online
		Meanwhile, I have just received a correspondence from reader Charlie Bryant alerting me to the following actual news release: "Emily Riehl, 17, of University High School in Bloomington, Ill., won the third-place $50,000 scholarship in a national science competition for her
		mathematics project expanding on geometric objects named for the French mathematician Jacques Tits.
		The project is titled "On the Properties of Tits Graphs."
	discuss.washingtonpost.com /wp-srv/zforum/02/weingarten032602.htm (2883 words)

	SFSU Algebra-Geometry-Combinatorics Seminar (Spring 2005)
		I will explain how compressed polytopes arise when statistical agencies try to protect confidential survey data.
		Abstract: Generalized polygons were introduced by Jacques Tits around 1960 in order to give geometric interpretations for all simple Lie groups and simple algebraic groups including the exceptional types.
		Among these polygons are generalized 3-gons, also called projective planes, which had been studied for a long time, but most fascinating are generalized 4-gons, also called generalized quadrangles, because they form the richest class.
	math.sfsu.edu /beck/seminar/seminar.s05.html (1082 words)

	Abstract (Site not responding. Last check: 2007-10-08)
		In his famous Lecture Notes of 1974, Jacques Tits gave a classification of (thick irreducible) spherical buildings of rank at least three.
		In joint work with Tits, these two projects have now been completed.
		We will give a brief overview of this work.
	www.mth.msu.edu /~mccarthy/colloq.03.spring/weiss.abstract.html (53 words)

	New Books for 02/14/2003 (Site not responding. Last check: 2007-10-08)
		Model categories and their localizations / Philip S. Hirschhorn.
		Moufang polygons / Jacques Tits, Richard M. Weiss.
		Rose, H. Linear algebra : a pure mathematical approach / Harvey E. Rose.
	www.nyu.edu /pages/cimslibrary/newbook/021403.html (1105 words)

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