1. Dr. M. S. Valiathan Memorial Lecture by Prof. M. S. Raghunathan
Title: Art That Would Rather Be Science
Abstract: In this talk, I will highlight the qualities of mathematics that it shares with art, making a case for it to be considered an art. On the other hand, it is often viewed with distaste by people in the arts, and the mathematician is more at ease in a milieu of scientists than in the company of artists.
2. Talk by Prof. N. S. Narasimha Sastry
Title: Classification of finite simple groups
Abstract: Each finite group is composed of a finite set of simple groups (with multiplicities) determined by the group, just like a positive integer determines (and is determined by) the set of prime numbers it is a product of. However, unlike the numbers, several finite groups may be composed of the same set of simple groups and their multiplicities.
Thus the importance of knowing all finite simple groups!
A very major mathematical achievement, mostly of 20th century, produced the complete list of finite (nonabelian) simple groups, up to isomorphism.
It is truly a marvelous that just the assumption that a finite group has no ntrivial normal subgroups, with sheer relentless logic of unparalleled proportion in the history of Mathematics (~1860 -2010), not only lead to the discovery of many - then unknown - simple groups and involved many exceptional mathematical situations, but also proved the completeness of the list of finite simple groups thus produced.
This work necessitated generation of a wealth of information about each of these groups such as: the subgroup structure, its representations, the 'natural geometry' it is the group of symmetries of, it's group extensions, etc.
Apart from enlarging our understanding of finite groups and facilitating the solution of many problems in group theory, the classification of finite simple groups also facilitated solving many problems in other areas of mathematics which are amenable to be reduced to problems about finite groups whenever such a problem could be further reduced to a question about finite simple groups.
Thus, the classification has been a powerful tool in finite groups both conceptually as well as from the perspective of applications.
A major, rather serendipitous, outcome of (the methods of) the classification is the discovery of the sporadic monster simple group. This beautiful, enigmatic, very group of symmetries, with its very intricate structure and its myriad connections to many areas of Mathematics
(modular forms, affine E_8 root system, k_3 surfaces, mock theta functions, string theory, discovered so far) seems to point towards themes unifying several areas of Mathematics.
Will try to give a brief account of the finite simple groups and mention some (easily statable, central, but deep and hopefully accessible) problems one can think about.
Will try to keep the talk simple and try to explain basic ideas.