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 E6 (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.F4-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.-
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.
In these articles, some of the currently very active mathematicians in the geometric, combinatorial and representation theoretic aspects of finite simple groups, Chevalley groups and their generalizations discuss the latest developments and major problems in their areas of research
The authors make an effort to make the articles accessible to graduate students and other potential new entrants to this very active field of research
This collection of articles represent the current status on several geometric aspects of Chevalley groups and their generalizations