Ritwik Mukherjee

I obtained my PhD in mathematics from Stony Brook UniversityI 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 will be teaching   M310 (Geometry of Curves and Surfaces)

Preprints and 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.               

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.

(submitted)

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



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

(This manuscript contains a self contained proof of the general position 
argument used in our paper on Hypersurfaces.)

Program to Enumerate Curves:

This is a sage program and is quite user friendly.  

(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.) 








Contact Information: 
email: ritwikm[at]niser.ac.in