I am currently interested in the moduli space and stack of curves and related questions in birational geometry (such as the Keel-Hassett program) as well as derived categories of these moduli spaces.
I have been interested in the results of Yogish Holla's paper Counting maximal subbundles via Gromov-Witten invariants and been trying to extend to the case of Parabolic Vector Bundles. Briefly, the problem is to count the number of maximal degree subbundles of a general stable vector bundle on a fixed nonsingular curve. The case for usual vector bundles was achieved by Yogish Holla using a version of Gromov-Witten invariants (equivalent to the more well-known version) which is a certain intersection number on a Quot scheme. This aforementioned Quot scheme has some nice properties tailor-made for carrying out the intersection. The way to handle the parabolic vector bundle case would be to find a counter part for this Quot scheme and a counterpart for the Vafa-Intriligator formula as used by Holla in his paper.
Summary of my time at Tata Institute of Fundamental Research, Mumbai, India (2020-2023) :
I am interested in Algebraic and Complex Geometry and was a student of Indranil Biswas and Yogish Holla for a short period of time.
During this time I studied different aspects of moduli spaces. Here is the link to my course overview report based on which I had to give a 1 hour talk in front of the Subject Board of Graduate Studies in Mathematics at TIFR Mumbai in June, 2022.
I had also been organizing and participating in student's seminars and Algebraic Geometry learning seminars at TIFR Mumbai. I had given a talk on the Moduli Spaces appearing in Algebraic Geometry. Here is a link to that article.