### Hi, I’m Sandip 👋

I am a research scholar at Indian Institute of Science Education and Research Kolkata in the Department of Mathematics and Statistics. It is my fourth year of the Integrated PhD program. I have been working under Dr. Somnath Basu. My broad area of research is Algebraic Topology, in paricular homological algebra and homotopy theory. I am also interested in Differential Geometry, Algebraic Geometry.

• ##### IISER Kolkata

Department of Mathemetics and Statistics

1. Equivalence Between Four Models of Associahedra
arXiv pre-print, 2022

1. PMRF
Selected under Prime Minister’s Research Fellows Scheme, May 2021 cycle
2. Gold Medalist, B.Sc.(Hons.)
Ranked first in order of merit among the successful candidates of B.Sc (Hons.) examination in Mathematics, Vidyasagar University.
Awarded for securing highest marks amongst all successful candidates in all honours examination in Arts, Science & commerce (Vidyasagar University)

1. Mathematics I (Teaching Assistant), October 2022 - December 2022
Upcoming...
2. NPTEL: Linear Algebra (Teaching Assistant), July 2022 - October 2022
Holding weekly problem solving sessions (online and live streamed in my youtube channel). All the pdfs of the notes are Here.
3. Mathematics II (Teaching Assistant), May 2022 - July 2022
Conducted weekly Tutorial Sessions and prepare sample questions.
4. NPTEL: Research Methodology (Teaching Assistant), January 2022 - May 2022
Evaluted assignments.
5. Probability I (Teaching Assistant), January 2022 - May 2022
Conducted weekly Tutorial Sessions, made question papers, evaluated Assignments, Mid-Sem, and End-Sem copies.
6. Linear Algebra I (Teaching Assistant), August 2021 - December 2021
Conducted weekly Tutorial Sessions and evaluated Quiz.
7. Analysis II (Teaching Assistant), January 2021 - May 2021
Conducted weekly Tutorial Sessions and evaluated Assignments.
8. Analysis I (Teaching Assistant), August 2020 - December 2020
Conducted weekly Tutorial Sessions, made question papers, evaluated Assignments, Mid-Sem, and End-Sem copies.

1. ##### IPhD Projects
1. Project I, Reeb's Theorem

In this project, we studied the Morse Theory and use it to prove Reeb's theorem, which states that if If $M$ is a compact manifold and $f$ is a $C^2$-function on $M$ with only two critical points, both of which are non-degenerate, then $M$ is homeomorphic to a sphere. We followed the book Morse Theory by John Milnor.

2. Project II, Morse Theory on Complex Grassmannian

Complex Grassmannian $G_k(\mathbb{C}^n)$ consists of all $k$ dimensional complex subspace in $\mathbb{C}^n$. It is a smooth (complex) manifold of real dimension $2k(n-k)$. Using Morse theory, we studied the cell structure of complex Grassmannian by constructing an explicit Morse function on it.

3. Project III, Cell Structure of Real and Complex Grassmannian

Here, we again studied the cell structure of complex Grassmannian topologically i.e., without using any smooth structure of complex grassmannian. This process is equally applicable for real Grassmannian too. Finally, we compare this cell structure of complex Grassmannian with that of obtained using Morse theory in project II.

4. Project IV, Cohomology Ring of Complex Grassmannian and Young Tableau

Using the CW-structure of the complex Grassmannian, we first compute the cellular homology of it and then cohomology by Poincaré duality. Finally, compute the cohomology ring structute of it using Young Tableau.

2. ##### Semester project in PDE and Distribution Theory

The two Trace Theorems in Sobolev spaces were studied. Detailed report can be found in the following link.

3. ##### Semester Project in Riemannian Geometry

Studied the proof of the theorem that any closed oriented surface of genus $g\geq 2$ admits metrics of constant negative curvature. Detailed can be found in the report with following link.