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This is the Proceedings of the ICM 2010 Satellite Conference on "Buildings, Finite Geometries and Groups" organized at the Indian Statistical Institute, Bangalore, during August 29 - 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups.

The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.

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1. On Characterizing Designs By Their Codes (B. Bagchi).- 2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen).- 3. Properties of a 27-dimensional Space of Symmetric Bilinear Forms Acted on by E 6 (R. Gow).- 4. On the Geometry of Global Function Fields, the Riemann-Roch Theorem, and Finiteness Properties of S -arithmetic Groups (R. Gramlich).- 5. Some Remarks on Two-Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lübeck).- 6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji).- 7. On Isotypies Between Galois Conjugate Blocks (R. Kessar).- 8. Representations of Unitriangular Groups (T. Le, K. Magaard).- 9. Hermitian Vernonesean Caps (J. Schillewaert, H. Van Maldeghem).- 10. On a Class of c.F 4 -geometries (A. Pasini).- 11. Buildings and Kac-Moody Groups (B. Rémy).- 12. Some Equations Over Finite Fields Related to Simple Groups of Suzuki and Ree Types (N.S. Narasimha Sastry).- 13. Oppositeness in Buildings and Simple Modules for Finite Groups of Lie Type (P. Sin).- 14. Modular Representations, Old and New (B. Srinivasan).- 15. The Use of Blocking Sets in Galois Geometries and in Related Research Areas (V. Pepe, L. Storme).- 16. Quadratic Actions (F.G. Timmesfeld).- Problem Set.-

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