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.

  • Elliptic curves and Galois representations
  • Algebraic number theory
  • Iwasawa theory
  • 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
  • Data Obfuscation for Microdata
  • Inferential Statistics

TRIM Members

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

Research Courses

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

  • 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 (Instructors: Dr. Anupam Mondal and Dr. Shion Samadder Chaudhury)
  • Graph Theory and Matroid – II (Instructors: Dr. Anupam Mondal and Dr. Shion Samadder Chaudhury)

Recent Publications

  • S. K. Mukherjee and S. Mukherjee: Generalized Larcombe–Fenessey invariants of matrix powers, Linear and Multilinear Algebra.
    Url: https://doi.org/10.1080/03081087.2022.2036087

  • 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 2022S.

  • S. ChaudhuryOn Quantum Evolving 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]