Mathematics as a subject has been shaped over ages through an intricate balance of fundamental research and practical applications, resulting in the seemingly disjoint disciplines termed as “pure” and “applied” mathematics. TRIM, however, focuses on foundational research in both fundamental and applied mathematics with the aim of translating research results to tangible contributions as is necessary for the modern realm of interdisciplinary advances in science and technology so that mathematics can reinvent itself by merging the long-term foundational impact of pure mathematics with short-term insightful gains from mathematical applications. The core mission of the Translational Research Institute in Mathematics (TRIM) is to foster and facilitate this holistic symbiosis. In a nutshell, TRIM will explore the benefits of translational research in mathematics by conducting cutting edge research in Mathematics with the focus on its applications to real-world problems arising out of industry needs, social-networking problems and communication science. Potentially, it shall re-invigorate the culture of mathematical thinking at the interface of theory and practice, by fostering excellence in higher education, capacity building. It shall encourage collaborative research with leading national and international institutes and technology-based industries. The group mostly, but is not restricted to, works in the following areas of specialization.

  • Functional Analysis
  • Operator Algebra
  • Commutative Algebra
  • (Non-) associative Algebras
  • Algebraic Topology
  • Low Dimensional Topology
  • Contact Topology
  • Knot Theory
  • Topological Combinatorics
  • Structural Graph Theory
  • Algebraic Graph Theory
  • Combinatorial and Discrete geometry
  • Discrete Morse Theory
  • Enumerative and algebraic combinatorics 
  • Matroid Theory
  • Lie algebra and Lie Groups
  • Deformation theory and Homotopy algebras
  • Algebraic Geometry


TRIM Members

The group is headed by Prof. Goutam Mukherjee. The team includes the following members.

Research Scholars


Research Courses

In the last two years, we have offered the following research courses offered from TRIM.

  • Linear Algebra and Multivariable Calculus (Instructors: Prof. Goutam Mukherjee and Dr. Satyendra Kr. Mishra)
  • Differentiable Manifolds and Vector Bundles (Instructors: Prof. Goutam Mukherjee and Dr. Kuldeep Saha) 
  • Cyclic Homology (Instructors: Prof. Goutam Mukherjee)
  • Analysis (Instructors: Dr. Somnath Hazra)
  • Commutative Algebra (Instructor: Dr. Satyendra Kr. Mishra) 
  • Introduction to Knot Theory and Low-dimentional Topology (Instructors: Dr. Apratim Chakraborty)
  • Combinatorics and Graph Theory – I and II (Instructors: Dr. Anupam Mondal and Dr. Sajal Kr. Mukhopadhyay)
  • Algebraic Topology (Instructors: Prof. Goutam Mukhopadhyay, Dr. Kuldeep Saha)
  • Algebra and Its Application (Instructors: Dr. Apratim Chakraborty and Dr. Kuldeep Saha)
  • Introduction to Probability and Statistics (Instructors: Prof. Rajeeva Laxman Karandikar, Dr. Debolina Ghatak)
  • Introduction to Stochastic Process (Instructors: Dr. Debapratim Banerjee)
  • Trends in Combinatorics and Topology (Instructors: Prof. Goutam Mukherjee, Dr. Sajal Mukherjee, Dr. Kuldeep Saha, Dr. Apratim Chakraborty and Dr. Anupam Mondal)
  • Topics in Knot Theory (Instructors: Dr. Apratim Chakraborty and Dr. Kuldeep Saha)
  • Graph Theory and Matroid – I and II (Instructors: Dr. Anupam Mondal and Dr. Shion Samadder Chaudhury)


Recent Publications

  • Sayan Chakraborty, Xiang Tang, Yi-Jun Yao, Smooth Connes-Thom Isomorphism, Cyclic Homology, and Equivariant Quantisation, Communications in Mathematical Physics (2024).

  • B. Banerjee and Goutam MukherjeeA Note on Cohomology of Clifford Algebras. Advances in Applied Clifford Algebras, Vol. 34 (16), 2024. Springer Nature Switzerland AG 2024. (doi: https://doi.org/10.1007/s00006-024-01324-z)

  • Saikat Goswami, Satyendra Kumar Mishra, Goutam Mukherjee: Automorphisms of Extensions of Lie-Yamaguti Algebras and Inducibility Problem. Journal of Algebra 641 (2024) 268–306.

  • Suratno Basu, S. Pal: Existence of Ulrich bundles on some surfaces of general type. Journal of Algebra, 640, 2024.

  • Suratno Basu, S. Pal: Stability of Sysyzy bundles corresponding to stable vector bundles on algebraic surfaces. Bulletin Des Sciences Mathematique, 189 (2023).

  • Sayan Chakraborty: Symmetrized non-commutative tori revisited. Journal of Noncommutative Geometry 2023. [arXiv]

  • Apratim Chakraborty, Anupam Mondal, Sajal Kr. Mukherjee, and Kuldeep Saha: On Elser’s conjecture and the topology of U-nucleus complex. Journal of Combinatorial Theory, Series A, 2023. Doi: https://doi.org/10.1016/j.jcta.2023.105748

  • A. Das, S.K.Hazra, Satyendra Kr. MishraNon-abelian extensions of Rota-Baxter Lie Algebras and inducibility of automorphisms. Linear Algebra and Its Application. Doi: https://doi.org/10.1016/j.laa.2023.04.005

  • A. Ghanwat, A. Nath, Kuldeep Saha: Relative LF embeddings of 4-Manifolds, Proc Math Sci 132, 52 (2022).
    Url: https://doi.org/10.1007/s12044-022-00686-3

  • A. Das, Satyendra Kr. Mishra: Bimodules over Relative Rota-Baxter Algebras and Cohomologies,Algebras and Representation Theory
    Url: https://doi.org/10.1007/s10468-022-10161-2

  • Kuldeep Saha, A. Nath: Open books and embeddings of smooth and contact manifolds, Advances in Geometry 2022

  • A. Das, Satyendra Kr. Mishra: The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators, Journal of Mathematical Physics 2022

  • Jishnu Ray, R. Sujatha: SELMER GROUPS OF ELLIPTIC CURVES OVER THE PGL(2) EXTENSION, Nagoya Mathematical Journal 2022

  • Apratim Chakraborty, J. B. Etnyre, H. Min: Cabling Legendrian and transverse knots.  Journal of Differential Geometry (to appear).

  • A. Ghanwat, Kuldeep Saha: On Embedding of 4-manifolds. Indian Journal of Pure and Applied Math (2021). [Link]