Rajagopalan had a habit that, once a week, no word will be uttered in the class. If the proposition is drawn on the board, you had to indicate what the hypothesis was, and you had to argue using your hands, without speaking a word, to reach the conclusion. Only through hand movement. It was quite a challenge, but Rajagopalan was a great teacher.

Adivarahan was the teacher who made the strongest impression. I remember the other teachers but they didn't make such a strong impression. Adivarahan was a legend in Loyola College and a very strict disciplinarian as well. A typical student would be scared to talk to him.

Raja also shared memories of his PhD years in Calcutta; he could not afford to either buy or xerox mathematics books. The only way to study them properly was to visit the university library and copy them by hand. When I expressed surprise at the amount of time this took, he explained that it actually helped him read more carefully and reflect deeply on the material - something that today's students, with their access to photocopiers and online downloads, might miss.

... the writer wishes to thank Dr V K Balachandran of the Indian Statistical Institute for several useful discussions during the preparation of the paper.

Many problems in probability theory, when properly formulated, appear as problems in the theory of convergence of stochastic processes. The need for such a theory was demonstrated by the early results of Doob, Donsker and others. In their fundamental papers, Le Cam and Prohorov developed several aspects of such a theory. Their work was based on, and was a development of, the earlier work of A D Alexandrov and Kolmogorov. However, several questions which naturally arise were either not discussed or discussed only under unnecessary restrictions. The following remarks contain an outline of a general theory of measures on topological spaces. Only the statements and the appropriate formulations of the main results are given. The detailed proofs will be published elsewhere.

This work was done during 1958-1959 while the author was in the Indian Statistical Institute, Calcutta, but due to diverse reasons the announcement was delayed up to now.

... attended the seminars of G W Mackey at the University of Washington at Seattle on the mathematical foundations of quantum mechanics and group representations. Already in 1954 as a first year undergraduate student he had the opportunity of listening to a talk by the eminent physicist P A M Dirac at Madras University. In the course of his lecture Dirac made the statement 'the world is noncommutative'. It was just as 'loud as a heartbeat' but its full significance came to light during the Mackey seminars. It was a meeting point of fundamental laws of nature, group representations, Lie groups and Lie algebras and probability theory. Raja had several long discussions with Mackey during which he mentioned that a deeper understanding of group representations must be sought in the 'formidable Lie algebraic machinery of Harish-Chandra'.

The purpose of this paper is to study a class of irreducible Banach space representations of a complex semi-simple Lie group G through an analysis of the associated representations of the Lie algebra $\mathfrak{g}$ of G.

The work described in this paper was done during 1963-65 when the authors were at the Indian Statistical Institute, Calcutta. At an early stage of the work, the last named author [Varadarajan] had the opportunity of detailed and highly stimulating discussions with Dr S R S Varadhan currently of the Courant Institute of Mathematical Sciences, New York. He would like to express his indebtedness to Dr Varadhan for these discussions which determined our entire approach to the whole circle of questions studied in the present work.

The present work is the first volume of a substantially enlarged version of the mimeographed notes of a course of lectures first given by me in the Indian Statistical Institute, Calcutta, India, during 1964-65. When it was suggested that these lectures be developed into a book, I readily agreed and took the opportunity to extend the scope of the material covered.

This period, 1963-65, was one of the most wonderful in my career. Calcutta was a very difficult place to live, with recurring power outages, rationing of essentials like rice and sugar, and other disruptions of daily life. The war in Vietnam was heating up and Calcutta, one of the most politicised centres in India, was in an uproar over this. The only constant was our work. We would work nonstop every day. We would read statements by Robert McNamara that it was only a matter of time before the war would end since half of Hanoi's electrical capacity was destroyed. We would laugh at this since we were always working in Calcutta much below capacity and yet the city and the people carried on heroically.

These notes are essentially the contents of a minicourse I gave at the Courant Institute in the fall of 2002. ... I have profited greatly from the lectures that Professor S Ferrara gave at UCLA as well as from many extended conversations with him, both at UCLA and at CERN, where I spent a month in 2001. ... I also gave a course in UCLA and a miniworkshop on supersymmetry in 2000 in Genoa, Italy, in the Istituto Nazionale di Fisica Nucleare.

At UCLA, with balanced emphasis upon research, exposition, teaching and mentoring he was a superb colleague who inspired respect and devotion among those lucky enough to work with him. He did sustained and significant work in at least five areas over his long career. ... At UCLA Raja found Richard Arens, Donald Babbitt, and Robert Blattner to be colleagues with sympathetic interests. Indeed, by that time Raja's primary interest was turning to the theory of semisimple Lie groups and their representations, and especially the transformative theory of Harish-Chandra who became a friend. Over the next 25 years, he and his collaborators T J Enright, J J Duistermaat, R Gangolli, J A C Kolk and P C Trombi, made diverse important contributions to this developing theory. Raja also wrote a number of excellent expository articles on Harish-Chandra's work. ... Inspired by problems arising from Harish-Chandra's theory, Raja collaborated with UCLA colleague Don Babbitt, from 1983 until 1991, in basic research on the theory of meromorphic differential equations with irregular singular points. They published six articles, and an Asterisque monograph in 1989 on the topic. This work brought him for the first time, as an active user, into contact with Grothendieck's theory of schemes and it had a lasting impact on his perspective. Around this time, Raja's concerns returned (they had never really left!) to quantum theory. He became interested in the new theory of quantum groups, in problems of quantisation, and in novel topics such as arithmetic, including non-archimedian, physics. He published numerous research and expository articles on all these topics, and hit high points with his 2004 exposition 'Supersymmetry for Mathematicians: an introduction', which became an AMS 'bestseller', and his 2006 collaborative paper which defined and developed the notion of a unitary representation of a Lie supergroup.

During this period, he supervised many graduate students, including myself. We would meet weekly for seminars on topics such as meromorphic differential equations, Lie algebras and their representations, quantum groups, and supersymmetry (SUSY). The series of seminars on SUSY was a collaborative effort with his long-time friend, Sergio Ferrara, from the physics department at UCLA. At that time, I was expecting my first child, Elia, and Raja humorously told me that my unborn child would already know mathematics simply by listening to our seminars. According to Hindu tradition, even unborn children can learn from their parents. Indeed, Elia did end up graduating in mathematics. Raja enjoyed spending time with his graduate students outside of work as well. His wife, Veda, would invite us to Thanksgiving dinners at the Varadarajans' home in Pacific Palisades, where we would relax in their beautiful garden, discuss mathematics, and, of course, enjoy their traditional Thanksgiving feast, featuring a huge turkey for the 20+ people in attendance. At these social gatherings, students had the chance to interact with other UCLA professors, such as his good friends Don Blasius and Robert Steinberg, in a casual atmosphere. Visiting professors from other universities would also join, creating a friendly environment that fostered valuable networking opportunities for students' future careers.

This volume is to be regarded as the fifth in the series of Harish-Chandra's collected papers, continuing the four volumes already published by Springer-Verlag. Because of manifold illnesses in the last ten years of his life, a large part of Harish-Chandra's work remained unpublished. The present volume deals with those unpublished manuscripts involving real groups, and includes only those pertaining to the theorems which Harish-Chandra had announced without proofs.

Raja and I shared many hours laughing and chatting. He had wide interests. For some years he took up the study of the clarinet, and enjoyed trying to play some snatches of Mozart's clarinet pieces, especially his Clarinet concerto K622. Shakespeare, The Mahabharata, Mozart, Bach, Wodehouse, Tin Tin, and the fortunes of the Los Angeles Lakers in the basketball championships were his unfailing passions.

Conversation with Raja was a unique delight. As all his friends witness, he had a remarkable memory of the vast range of his experiences. He also had a strong interest in the lives of mathematicians and he knew many stories and quotes. ... For two decades he and Veda have been a prime source of recommendations for mysteries, especially classic British crime fiction, including those on television. Once, to start the conversation, I mentioned that I had seen an episode of the British series 'Midsomer Murders' the night before. He perfectly recalled the plot of the episode, which he had seen years before, and even corrected me on a point.

UCLA has received $1 million from mathematics professor emeritus V S Varadarajan and his wife, Veda, to establish the Ramanujan Visiting Professorship in his home department. The new position honours renowned Indian mathematician Srinivasa Ramanujan, who made substantial contributions to mathematics in the early 1900s. The post will help UCLA attract visiting faculty members in Varadarajan's specialisations of automorphic forms, an important concept in number theory, and representation theory, which has been linked to elementary particles and quantum physics.