**Date & Time:** Wednesday, September 16, 2015, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** Ritwik Mukherjee, TIFR Mumbai

**Title:** Enumerative Geometry of rational cuspidal curves on del-Pezzo
surfaces

**Abstract:** Enumerative geometry is a branch of mathematics that deals
with the following question: "How many geometric objects are there that
satisfy certain constraints?" The simplest example of such a question is
"How many lines pass through two points?". A more interesting question
is "How many lines are there in three dimensional space that intersect
four generic lines?". An extremely important class of enumerative question
is to ask "How many rational (genus 0) degree d curves are there in
CP^2 that pass through 3d-1 generic points?" Although this question
was investigated in the nineteenth century, a complete solution to this
problem was unknown until the early 90's, when Kontsevich-Manin
and Ruan-Tian announced a formula. In this talk we will discuss some
natural generalizations of the above question; in particular we will be
looking
at rational curves on del-Pezzo surfaces that have a cuspidal singularity.
We
will describe a topological method to approach such problems in Enumerative
Geometry.