Studying moduli spaces of stable maps and quantum cohomology theory plays a prominent role in modern enumerative geometry. A landmark result in this area is Kontsevich’s recursion formula to enumerate rational curves in
projective space.
In this talk, we shall speak about the enumeration of plane rational curves with an ordinary m fold point (joint work with Indranil Biswas, Ritwik Mukherjee, Chitrabhanu Chaudhuri, and Apratim Choudhury). In particular, we shall explain our approach to the following question: how many rational degree d curves are there in CP2 that have an m-fold singular point and that passes through 3d+ 1−m generic points? Earlier approaches solved this question only for m = 3. The question was practically beyond reach for m ≥ 4. We have managed to solve this question for all m by simply developing a family version
of Kontsevich’s recursion formula. If time permits, we shall discuss some future problems.
Zoom link: https://icts-res-in.zoom.us/j/83482036629?pwd=8T3pl2QUwcYff11EjOuN0Qriy5yqAe.1
Meeting ID: 834 8203 6629
Passcode: 887430