# Ritwik Mukherjee

I obtained my PhD in mathematics from Stony Brook University. I am presently a Reader-F at NISER.

My research interests are Enumerative Geometry using Topological methods.

Here is a brief description of my research and my CV.

**Teaching: **

Fall 2016: I was teaching M304 (Topology).

Spring 2017: I was teaching M404 (Algebraic Topology).

Fall 2017: I was teaching M306 (Calculus of Severable Variables).

Spring 2018: I was teaching M404 (Algebraic Topology).

Fall 2018: I was teaching M483 (Introduction to Manifolds).

Spring 2019: I was teaching M102 (Introduction to Mathematics 2).

Fall 2019: I was teaching M201 (Real Analysis)** ** and M555 (Harmonic Analysis)

Spring 2020: I was teaching M310 (Geometry of Curves and Surfaces)** (**cut short due to the COVID situation**) **

Fall 2020: I am currently teaching M483 (Introduction to Manifolds)** (**conducted online due to the COVID situation **)**

**Published (or accepted) Papers:**

** **Enumeration of rational curves in a moving family of P^2. Here is the link to the journal site.

(Published by Bulletin des Sciences Mathématiques) Here is the arXiv version.

Rational cuspidal curves on del-Pezzo surfaces Here is the link to the journal site.

(Published by Journal of Singularities) Here is the arXiv version.

Genus two enumerative invariants in del-Pezzo surfaces. Here is the link to the journal site.

(Published by Geometriae Dedicata) Here is the arXiv version.

Genus one enumerative invariants in del-Pezzo surfaces. Here is the link to the journal site.

(Published by Comptes Rendus Mathématique) Here is the arXiv version.

Enumeration of curves with one singular point. Here is the link to the journal site.

(Published by Journal of Geometry and Physics) Here is the arXiv version.

Enumeration of curves with two singular points. Here is the link to the journal site.

(Published by Bulletin des Sciences Mathématiques) Here is the arXiv version.

**Preprints: **

Counting planar curves in P^3 with degenerate singularities. Here is the arXiv version.

Rational cuspidal curves in a moving family of P^2. Here is the arXiv version.

Counting curves in a linear system with upto eight singular points. Here is the arXiv version.

Collision of upto seven singular points.

(in preparation)

Enumeration of singular hypersurfaces on arbitrary complex manifolds. Here is the arXiv version.

Counting curves on a general linear system with upto two singular points. Here is the arXiv version.

(submitted)

Probability distribution of constrained Random Walks. Here is the arXiv version.

**Notes: **

Enumeration of curves with singularities: Further details

(This manuscript contains a few straightforward details that were omitted from our papers.)

Enumeration of singular hypersurfaces: general position arguments

(This manuscript contains a self contained proof of the general position

argument used in our paper on Hypersurfaces.)

**Program to Enumerate Curves:**

Mathematica program to enumerate curves with at most seven singular points in CP^2

Interactive website to directly enumerate curves with one singular point in CP^2.

(This is a sage program and is quite user friendly)

Mathematica program to enumerate curves with upto seven singular points in a general Linear System

(Here is a pdf file of the output)

(The recursive formula in this program is slightly different from the previous program; the final formula is the same

in both the cases.)

Mathematica program to enumerate curves with upto eight singular points in a general Linear System

(Here is a pdf file of the output.)

C++ program to enumerate rational cuspidal curves on del-Pezzo surfaces (source code)

Haskell program to enumerate rational cuspidal curves on del-Pezzo surfaces (source code)

Mathematica program to count the number of genus 0 planar curves in P^3

Mathematica program to count the number of genus 0 planar cuspidal curves in P^3

Mathematica program to count planar degree d curves in P^3 with singularities till codimension 4

**Contact Information: **

email: ritwikm[at]niser.ac.in