This proceedings volume contains chapters presented at the International Conference on Lie Algebras and Number Theory (ICLANT-2024), held at the Department of Mathematics, National Institute of Technology Calicut, Kerala, India, from 10–14 June 2024. It discusses recent research on Lie algebras and number theory and studies their applications in several areas in mathematics and physics. Chapters in the book address the representation theory of Lie algebras, superalgebras and number theory. The book aims to emphasize the diversity of Lie theory and its applications to other branches of mathematics, in particular number theory and other areas of physics.

M. Ram Murty is the Queen’s Research Chair and A. V. Douglas Distinguished University Professor at Queen’s University, Canada, where he is also cross-appointed to the Department of Philosophy and teaches courses in mathematical logic and Indian philosophy. Previously, he was a professor at McGill University (1982–1996), and earned his Ph.D. from MIT in 1980, followed by postdoctoral fellowships at the Institute for Advanced Study, Princeton, and the Tata Institute of Fundamental Research in Mumbai. He is a Fellow of the Royal Society of Canada, the Fields Institute, the Indian National Science Academy, the American Mathematical Society, and the Canadian Mathematical Society. His honors include the E.W.R. Steacie Fellowship, Killam Research Fellowship, Simons Fellowship, and the 2024 CRM-Fields-PIMS Prize. A prolific scholar, he has published over 300 research papers and 15 books, and supervised more than 25 doctoral students, 50 master’s students, and 50 postdoctoral fellows. His introductory book on Indian philosophy was published by Broadview Press.

Saudamini Nayak is Assistant Professor in the Department of Mathematics at the National Institute of Technology Calicut, India. She obtained her Ph.D. from the National Institute of Technology Rourkela, India (2017). She did her Post-Doctoral work at Harish-Chandra Research Institute Prayagraj, Allahabad, India and the Institute of Mathematics and Applications, Bhubaneswar, India. Her broad area of research is Lie algebras and superalgebras. She is mostly interested in structure and representation theory of finite and infinite dimensional Lie algebras (superalgebras).

Chiranjit Ray is Assistant Professor in the Department of Mathematics at the National Institute of Technology Calicut (NITC), India. He earned his Ph.D. from IIT Guwahati in 2019 and subsequently held postdoctoral positions at the Harish-Chandra Research Institute and the Indian Statistical Institute Delhi, supported by the Department of Atomic Energy, India. Before joining NITC, he served as an Assistant Professor at IIIT Sri City. His research focuses on number theory, particularly partition theory, modular forms, hauptmoduls, and Siegel cusp forms. He has published extensively and actively engages in collaboration and mentoring to promote mathematical research.

Sudhansu Sekhar Rout is Assistant Professor in the Department of Mathematics at the National Institute of Technology Calicut, India. Prior to that he was working as Assistant Professor at the Institute of Mathematics and Applications, Bhubaneswar, Odisha. He obtained his PhD from the National Institute of Technology Rourkela, India (2016). He did his Post-Doctoral work at Harish-Chandra Research Institute Prayagraj, Allahabad, India (2017). His broad research area of research is number theory. His research interests include Diophantine equations, S-units in recurrence sequences, special values of zeta functions, arithmetic of dynamical systems. He has published papers in several journals of repute, and he is actively involved in supervising Ph.D. and master’s students.

Eswara Rao Senapathi is formerly faculty at the Tata Institute of Fundamental Research, Mumbai, until 2017. He did his master’s in mathematics in 1978 and stood first. He did his postdoctoral in the University of Saskatchewan, Canada, for two years with one year as faculty. His research interests are in Kac–Moody Lie algebras and toroidal Lie algebras. He published 46 papers in reputed journals like Transactions American Mathematical Sciences and Communications of Mathematical Sciences. His citation index is more than 800 in MathSciNet. Even after his retirement, he is actively doing research and guiding students and publishing research papers.