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, focusses 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
  • 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
  • (Non-) associative Algebras
  • 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

  • Saikat Goswami, Junior Research Fellow (3rd Year)
  • Shital Lawande, Junior Research Fellow (3rd Year)
  • Tamojit Saha, Junior Research Fellow (3rd Year)
  • Swarup Kumar Das, Junior Research Fellow (2nd Year)
  • Aninda Banerjee, Junior Research Fellow (2nd Year)
  • Pratik Kumar Kundu, Junior Research Fellow (2nd Year)
  • Pritam Chandra Pramanik, Junior Research Fellow (2nd Year)
  • Jyotirmay Das, Junior Research Fellow (2nd Year)
  • Sneha Banerjee, Junior Research Fellow (1st Year)
  • Sucharita Barik, Junior Research Fellow (1st Year)
  • Abhirup Das, Junior Research Fellow (1st Year)
  • Madhura Dutta, Junior Research Fellow (1st Year)
  • Umme Joinab, Junior Research Fellow (1st Year)
  • Sandip Mandal, Junior Research Fellow (1st Year)
  • Suman Pattanayak, Junior Research Fellow (1st Year)
  • Arundhati Rakshit, Junior Research Fellow (1st Year)
  • Subhadeep Rana, Junior Research Fellow (1st Year)


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

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

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

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

  • S. S. ChaudhuryOn Quantum Evoling Secret Sharing Schemes – Further Studies and ImprovementsQuantum Information and Computation (2021).

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

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