AIS - Operator Theory and Operator Algebras (2026)

Venue: IIT, Roorkee

Dates: 15 Dec 2026 to 27 Dec 2026


Convener(s)

 
Name:  Prof. Jaydeb Sarkar   Dr. Arup Chattopadhyay  Dr. Amit Maji
Mailing Address: Professor-in-Charge
(Head of the Division),
Statistics and Mathematics Unit, ISI Bangalore, 
Bangalore– 560059, Karnataka, India

Associate Professor,
Department of Mathematics,
IIT Guwahati,
North Guwahati, Assam, India, 781039.

Associate Professor
Department of Mathematics
Indian Institute of Technology Roorkee
Roorkee-247 667, Uttarakhand, India
Email: jaydeb at gmail.com  arupchatt at iitg.ac.in amit.maji at ma.iitr.ac.in 

Operator algebras and operator theory, central areas of functional analysis, interact significantly with fields such as topology, complex analysis, harmonic analysis, and group theory. Originally motivated by problems in quantum mechanics and spectral theory, these subjects provide a powerful framework for studying linear operators on Hilbert and Banach spaces. Over time, they have also played a crucial role in fields such as non-commutative geometry, representation theory, and mathematical physics.

The aim of this programme is two-fold. We start with the basics of functional analysis and operator theory, which includes topics in C^*-algebras and basic of Hardy space theory. Then we move our discussion to a part of multivariable operator theory, namely dilation theory and Nevanlinna-Pick interpolations, a classical topic in modern operator theory. In the second part, we will discuss some basics of von Neumann algebras, including the GNS construction. At the end, we will give a brief flavour of trace formulae in operator theory as a part of non-commutative analysis.

This AIS program is aimed at postgraduate and Ph.D. students. It will introduce key classical and modern developments through mini-courses and problem sessions. The courses will be largely self-contained and accessible, requiring only a basic background in complex analysis and functional analysis.