Sandip Samanta pic taken at IIT Bomaby

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 sixth 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.

Education & Certifications
  • IISERK Logo
    IISER Kolkata

    Department of Mathemetics and Statistics

  1. Equivalence Between Four Models of Associahedra
    Basu, Somnath, and Samanta, Sandip
    arXiv preprint, 2022
  2. On the James brace product: generalization, relation to $H$-splitting of loop space fibration & the $J$-homomorphism
    Basu, Somnath, and Bhowmick, Aritra, and Samanta, Sandip
    arXiv preprint, 2024

  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.
  3. Sukumari Gupta Smriti Puraskar
    Awarded for securing highest marks amongst all successful candidates in all honours examination in Arts, Science & commerce (Vidyasagar University)

  1. NPTEL: GATE Mathematics Live session, August 2023 - February 2024, NPTEL
    Conducting weekly problem solving sessions (online) on previous year GATE Mathematics problems. All the pdfs of the notes are available here.
  2. NPTEL: Point Set Topology (Teaching Assistant), January 2023 - April 2023, NPTEL
    Conducting weekly problem solving sessions (online). Recorded videos are available in my youtube channel. All the pdfs of the notes can be found here.
  3. Mathematics I (Teaching Assistant), October 2022 - December 2022, IISER Kolkata
    Conducted weekly Tutorial Sessions and graded the class test, Mid-Sem and End-Sem copies.
  4. NPTEL: Linear Algebra (Teaching Assistant), July 2022 - October 2022, NPTEL
    Conducted weekly problem solving sessions (online). Recorded videos are available in Youtube and all the pdfs of the notes are available Here.
  5. Mathematics II (Teaching Assistant), May 2022 - July 2022, IISER Kolkata
    Conducted weekly Tutorial Sessions and prepare sample questions.
  6. NPTEL: Research Methodology (Teaching Assistant), January 2022 - May 2022, NPTEL
    Evaluted assignments.
  7. Probability I (Teaching Assistant), January 2022 - May 2022, IISER Kolkata
    Conducted weekly Tutorial Sessions, made question papers, evaluated Assignments, Mid-Sem, and End-Sem copies.
  8. Linear Algebra I (Teaching Assistant), August 2021 - December 2021, IISER Kolkata
    Conducted weekly Tutorial Sessions and evaluated Quiz.
  9. Analysis II (Teaching Assistant), January 2021 - May 2021, IISER Kolkata
    Conducted weekly Tutorial Sessions and evaluated Assignments.
  10. Analysis I (Teaching Assistant), August 2020 - December 2020, IISER Kolkata
    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.

  1. Invited Talks
    1. $H$-splitting in Loop Space Fibration, Bengal Topology Circle Meeting 2023, TCG-CREST, 20th January, 2023
  2. Contributed Talks
    1. $H$-splitting in Loop Space Fibration, GROOT Summer Seminar, Online, 28th June, 2023
    2. $H$-splitting in Loop Space Fibration and Brace Product, Inter IISER-NISER Mathematics Meet (IINMM) 2023, NISER Bhubaneswar, 30th September, 2023

  1. Hedra Zoo (based on our arXiv preprint) DMS Symposium 2022, IISER Kolkata, February, 2022