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Research and Expository Publications in Mathematics

 

 

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In the pipeline

"A Local Approach to Twin Buildings", preprint.

Lectures on Buildings, in a new edition, revised and updated, University of Chicago Press (to appear 2009).

"Construction and Automorphisms of Buildings", in: Essays in Geometric Group Theory (ed. N.S. Narasimha Sastry), Ramanujan Mathematical Society Publications (to appear 2009) 125–143.

Published

"Buildings", in The Princeton Companion to Mathematics (ed. Tim Gowers), Princeton Univ. Press. (2008) 161–162.

"Lie Theory", in The Princeton Companion to Mathematics (ed. Tim Gowers), Princeton Univ. Press. (2008) 229–234.

"Quadrangular Algebras by Richard M. Weiss" A review in the Bulletin of the Amer. Math. Soc. 45 (2008) 315–319.

Symmetry and the Monster: one of the greatest quests in mathematics, Oxford University Press, 255 pages, hardback 2006, paperback 2007.

"From Galois and Lie to Tits Buildings", The Coxeter Legacy: Reflections and Projections (ed. C. Davis and E.W. Ellers), Fields Inst. Publications volume 48, American Math. Soc. (2006), 45–62.

"Topological groups of Kac-Moody type, right-angled twinnings and their lattices" (with B. Rémy), Comment. Math. Helv. 81 (2006), 191–219.

"Modern Algebra", Encyclopedia Britannica On-line (2005).

"Linear Algebra", Encyclopedia Britannica On-line (2005).

"Multiple Trees", J. Algebra 271 (2004), 673–697.

"Classification of Buildings", Finite Groups 2003: Proc. of Gainsville Conf. on Finite Groups, (ed. C.Y. Ho, P. Sin, P.H. Tiep, A. Turull), de Gruyter, Berlin-New York 2004, 319-333.

"Affine Twin Buildings", J. of London Maths. Soc. 68 (2003), 461–476.

"Twin Trees and Twin Buildings", in Tits Buildings and the Model Theory of Groups, (ed. K. Tent), LMS Lecture Note Series 291, 119-137, Cambridge University Press, 2002.

"Local Isometries of Twin Buildings," Math. Zeitschrift 234 (2000), 435–455.

"Twin Trees II: Local Structure and a Universal Construction" (with J. Tits), Israel J. Math. 109 (1999), 349–377.

"A characterization of twin buildings by twin apartments" (with P. Abramenko), Geo. Ded. 73 (1998), 1–9.

"Local to Global Structure of Twin Buildings" (with B. Muehlherr), Inventiones Math. 122 (1995), 71–81.

"Twin Trees I" (with J. Tits), Inventiones Math. 116 (1994), 463–479.

"Buildings and their applications, I. Basic ideas", Bull. London Math. Soc. 24 (1992), 1–51.

"Buildings and their applications, II. Affine buildings and symmetric spaces", Bull. London Math. Soc. 24 (1992), 97–126.

"Symmetry and the Monster", Interdisciplinary Science Reviews 17 (1992), 56–62.

"Classification and Construction of Buildings", in Finite Geometries, Buildings, and Related Topics, (ed. W.M. Kantor), 1-15, Oxford Univ. Press, 1990.

Lectures on buildings, Perspectives in Mathematics 7, Academic Press, 1989.

"Computation of presheaf homology and 2-modular representations for A7, A8, and M24" (with S. D. Smith), Comm. Algebra 17 (1989), 1199–1237.

"Duality for presheaves on chamber systems, and a related chain complex", J. Algebra 121 (1989), 263–274.

"Building buildings" (with J. Tits), Math. Ann. 278 (1987), 291–306.

"Embeddings and hyperplanes of discrete geometries", Europ. J. Combin. 8 (1987), 179–185.

"Universal presheaves on group geometries and modular representations" (with S. D. Smith), J. Algebra 102 (1986), 135–154.

"A construction of buildings having no rank 3 residues of spherical type", Proc. of 1984 C.I.M.E. conference (Buildings and Diagram Geometries), Springer Lect. Notes 1181 (1986), 242–248.

"Extending locally truncated buildings and chamber systems", Proc. London Math Soc. 53 (1986), 385–406.

"Buildings and sporadic groups", Contemp. Math. 45 (1985), 295–301.

"Sheaves on buildings and modular representations of Chevalley groups" (with S. D. Smith), J. Algebra 96 (1985), 319–346.

"Triangle geometries", J. Combin. Theory 37 (1984), 294–319.

"Minimal parabolic geometries for the sporadic groups" (with G. Stroth), European J. Combin. 5 (1984), 59–91.

"Embeddings of group geometries and modular representations", Proc. of the Rutgers Group Theory Year 1983-84, Cambridge, 1984.

"Locally truncated buildings and M24", Math. Z. 180 (1982), 489–501.

"On the second homotopy group of certain simplicial complexes and some combinatorial applications", Quart. J. Math. Oxford 32 (1981), no. 2, 225–233.

"On buildings and locally finite Tits geometries" (with U. Ott), London Math. Soc. Lecture Notes 49 (1981), 272–274.

"Coverings of certain finite geometries", London Math. Soc. Lecture Note Ser. 49 (1981), 316–331.

 "A combinatorial characterization of the dual Moufang hexagons", Geom. Dedicata 11 (1981), 61–67.

"A geometric characterization of Moufang hexagons", Invent. Math. 57 (1980), 227–262.

"Semi-regular graph automorphisms and generalized quadrangles", J. Combin. Theory Ser. A29 (1980), 319–328.

"A note on the 3D4(q) generalized hexagons", J. Combin. Theory Ser. A29 (1980), 249–250.

"2-local geometries for some sporadic groups" (with S. D. Smith), Proc. Symp. Pure Math. 37 (1980), 283–289.

"Coverings and automorphisms of chamber systems", European J. Combin. 1 (1980), 259–269.