Abstract: My travels on the LS (Lakshmibai-Seshadri) path have brought many personal realizations and its vistas have allowed me to look out over many beautiful structures. As best I can, I shall give a brief summary (1 hour instead of 20 years) including: Kashiwara crystals, combinatorial aspects of Schubert calculus, affine Hecke algebras and structure of Chevalley groups.

Michel Brion, *The cohomology algebra of an algebraic group.*

Corrado DeConcini, *Index, infinitesimal Index of transversally elliptic operators and splines.*

Claudio Procesi, *Algebraic and geometric aspects of the non linear
Schroedinger equation*

C.S. Rajan, *Spectrum and Arithmetic*

Patrick Polo, *On torsion in integral intersection cohomology of Schubert varieties*

Ravi Vakil, *Stabilization of discriminants in the Grothendieck ring*

N. Mohan Kumar, *Spaces of rational curves in general hypersurfaces.*

Adrian Langer, *On a positive equicharacteristic version of the
Grothendieck-Katz conjecture*

Constantin Teleman, *Geometric Langlands correspon- dence after
Beilinson-Drinfeld and deformed opers*