REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Venkatramani Lakshmibai

ABSTRACT:  Seshadri introduced " vector bundles with parabolic structures " on a compact Riemann surface in late 1960s while studying the moduli of vector bundles on curves. Such bundles were found to be of great importance in Mathematical Physics - especially in Quantum and Conformal field theories in the 1980s and 1990s. Recently (in late 1990s and 2000s), such bundles were found to play a crucial role in the study of coherent sheaves on the projective line. In this talk, we shall first introduce " vector bundles with parabolic structure " on a compact Riemann surface (a la Seshadri). We shall then see some applications of such bundles - mainly, the recent works of Crawley-Boevey on "Weighted Projective Lines" and "Deligne-Simpson Problem".