**Ritwik Mukherjee**

TIFR

March 5, 2015

**Enumerative geometry of singular curves in a general linear system**:
Enumerative geometry of singular plane curves (i.e. curves in $CP^2$) is a classical subject dating back to nineteenth century. A more general class of question is to consider a general linear system $L--->X$ over a compact complex manifold and enumerate singular curves in this linear system. In this talk we will describe a topologcial method to approach questions of this nature. The basic idea is to express these enumerative numbers as the Euler class of some appropriate bundle. If time permits, we will give a brief idea about how to compute degenerate contributions to the Euler class using topological methods.