VOLUME V ISSUE 1 NEWS 2019 TATA INSTITUTE OF FUNDAMENTAL RESEARCH photograph by Peter Badge | www.abelprize.no Wall plaque at the ICTS Campus, Bangalore. REMEMBERING MICHAEL ATIYAH ICTS Address Survey No. 151, Shivakote village, Hesaraghatta Hobli, North Bengaluru, India 560089 Website www.icts.res.in 1 VOLUME V NEWS ISSUE 1 2019 TATA INSTITUTE OF FUNDAMENTAL RESEARCH L R: C. Musili, C.S. Seshadri, M.S. Narasimhan, M.S. Raghunathan and David Mumford at TIFR (1968) ⟶ www.cmi.ac.in/~ramadas/NS@50/ tifr archives Michael Atiyah lecturing at TIFR tifr archives Michael Atiyah during his visit to TIFR, Mumbai, in 1984. MICHAEL ATIYAH M.S. NARASIMHAN & C.S. SESHADRI M.S. NARASIMHAN mathematical aspects of gauge theory arising in of holomorphic vector bundles on the Riemann Sir Michael Atiyah was a great mathematician theoretical physics. surface which have been studied earlier by Seshadri who made path-breaking contributions to various and myself. This work of Atiyah and Bott was very His best known result is the celebrated Atiyah- fields in mathematics and played a crucial role in influential and popularised these moduli spaces Singer index theorem, which is a vast generalisation promoting the resurgence of contact between among physicists. of famous results like the Riemann-Roch theorem mathematics and theoretical physics in the latter and which is intimately related to K-Theory. A He had an effervescent and inspiring personality. half of the twentieth century. major related work is the Atiyah-Patodi-Singer He valued collaboration in mathematics and loved He was the recipient of many honours, including index theorem, which deals with elliptic operators intense mathematical discussions. He seemed to the Fields Medal and the Abel Prize. His work on manifolds with boundary and non-local derive many of his insights and ideas in the process combined creatively Analysis, Differential boundary conditions. (A version of the Hirzebruch of talking. Geometry and Topology. His major contributions signature theorem for manifolds with boundary) I maintained a close and fruitful contact with him have been to Topological K-Theory (which proved Atiyah and Bott made an extensive study of over the years and we had several conversations to be a remarkably powerful tool in Topology), the Yang-Mills equation on compact Riemann on moduli problems and some aspects of the index Index Theorem for linear elliptic operators and surfaces and its relationship to the moduli spaces theorem. Moreover, many of my best students did www.icts.res.in 2 | ICTS NEWS | VOLUME V | ISSUE 1 2019 3 their post-doctoral study with Atiyah, the best C.S. SESHADRI earliest to perceive the importance of NS and let his “… The fact that I had physics friends is an known example being Vijay K. Patodi. Patodi’s I had heard of Michael Atiyah as a brilliant student student Newstead to calculate the cohomology of indication that the frontiers between disciplines stay in Princeton, working with Atiyah, resulted of Hodge when I was a graduate student at the certain “moduli spaces” figuring in NS. Theory needs were breaking down, and this has become the in his celebrated joint work with Atiyah, Bott and Tata Institute of Fundamental Research (TIFR). main feature of our times. The old rigid disciplines Newstead got a position in Liverpool and a framework Singer. (Atiyah and I later edited the Collected of the past are giving way to a much more fluid Then I came across his paper on the classification of Atiyah arranged for a visit to Liverpool by Papers of Patodi. In the foreword Atiyah wrote in which to scene, which is why the ICTS is the right body for vector bundles on Elliptic Curves. This attracted me M. S. Narasimhan and me. Atiyah again perceived that the work of Atiyah-Patodi-Singer ‘was the future. The future belongs to the young and the since Grothendieck had classified vector bundles on the importance of “moduli spaces of parabolic a great collaboration, exploiting the different develop and, as a science that is now emerging will affect the lives of the projective line and I noticed in my thesis that vector bundles” – a work I had done with Vikram talents of the participants.’) everyone on the planet. The ICTS has a noble task, ’s result is a consequence of an early Mehta (i.e. the geometry and physics of knots, Grothendieck mathematician, that of providing the right atmosphere to inspire I will mention a few recollections of my work of G.D. Birkoff. by Atiyah). I met Atiyah several times during the next generation of scientists …” ■ mathematical interactions with him. The original 1975–76, at the Institute for Advanced Study, I believe that In 1957, I proved that a finitely generated proof of the Atiyah-Bott fixed point theorem Princeton, TIFR Colloquium on vector bundles, Read the full text of the speeches here: projective module over the ring of polynomials mathematics used a result of Takeshi Kotake and myself on 1982, sometime in Bonn when he expressed his https://bit.ly/Atiyah_ScienceAtICTS_Speech in two variables is free (the first non-trivial case fractional powers of linear elliptic operators. great regard for Patodi. provides https://bit.ly/Atiyah_ScienceAtICTS_youtube of Serre’s problem). I attended the International Atiyah asked me to give a talk on this result. On https://bit.ly/Atiyah_FoundationStoneRemarks Congress held at Edinburgh in 1958 and remember It is a great privilege for having known Atiyah and another occasion, during an Arbeitstagung in that unifying conversing with during a cruise trip at this to have had his interest in my work. ■ Bonn, I told him about the canonical filtration Atiyah Congress. He told me that a British mathematician Michael Atiyah delivers the ceremonial speech for framework … which Harder and I had introduced on vector M. S. Narasimhan and C. S. Seshadri are eminent the ICTS Inauguration Event: Science at ICTS (whose name I forget) also solved Serre’s problem bundles on curves and suggested that it could mathematicians, well known for the famous for two variables but found that I had already was a nice problem that taught me that at times be of use in the work on Yang-Mills equation on Narasimhan-Seshadri theorem.They were among will contain mathematically oriented scientists. Spenta R. Wadia is a theoretical physicist and the done this earlier. Atiyah was the star attraction in a path integral it is necessary to sum over both Riemann surfaces he was undertaking at that the main pillars of the famed School of Mathematics So the exact allocation is not important, so long as Founding Director, Infosys Homi Bhabha Chair at the International Conference on Differential stable and unstable classical solutions to obtain the flexibility and quality are maintained. time with Bott. of TIFR, where they spent most of their professional Professor and Professor Emeritus at ICTS–TIFR, Analysis in 1964 at TIFR. A few months later, the correct answer. I did not publish this result as my life. Narasimhan later spent some years building Bengaluru His passing is a great loss for the mathematical Narasimhan-Seshadri theorem (NS) was proved. Finally, I totally agree that your initial appointments mathematics at ICTP and Seshadri founded the PhD mentor Bunji Sakita had emphasized that one community. M.S. Narasimhan gave a talk at this conference should be made cautiously and not in haste.” Chennai School of Mathematics. should write up only very substantive papers! In on an ingredient of NS. Atiyah was among the retrospect I think it would have been been valuable He embraced the idea and purpose of the ICTS, which to publish this simple result. he put forth in his remarks for the Foundation Stone BETWEEN THE Ceremony of ICTS on 28 December 2009, Michael also played an important role in the SCIENCE “Science has the noble aim of trying to understand establishment of the ICTS. The committee he the natural world in human terms: to make sense chaired that reviewed Mathematics at the Tata REMEMBERING MICHAEL FRANCIS ATIYAH of what we see. This brief phrase encapsulates both Institute of Fundamental Research (TIFR) in 2005 ABHIRUP GHOSH’ s submission towards theory and experiment. What we see, in the broad made a strong recommendation for an interactive the Augmenting Writing Skills for Articulating sense, covers experiment and making sense is the program for physicists and mathematicians. This Research (AWSAR) Award 2018, organised by (1929-2019) task of theory. As the great French mathematician reinforced the recommendation of the Theoretical the Department of Science and Technology Henri Poincare said, science is no more a collection of SPENTA R. WADIA Physics review committee in 2006 to establish ICTS (DST), Government of India, has been facts than a house is a collection of bricks: it requires in 2007. selected among the top 100 entries.. theory to hold it together. Michael Francis Atiyah, one of the most significant 3-dimensional topology. String theory embodies He was deeply interested in bringing the math and He strongly supported the idea of creating the ICTS Theory needs a framework in which to develop and, ADHIP AGARWALA’s PhD thesis titled mathematicians of the second half of the 20th this essential unity in a natural way. physics communities together to talk and share. and was a member of its International Advisory as a mathematician, I believe that mathematics ‘Excursions in ill condensed quantum matter: century, passed away on 11th January 2019. His His enthusiasm was infectious. He attributed his Board from inception till his passing away. His active During my tenure at the Enrico Fermi Institute, provides that unifying framework … from amorphous topological insulators profound contributions to topology, geometry interest in physics to his collaborator and friend involvement and advice has been encouraging and Michael visited the University of Chicago for a to fractional spins’ has been selected by and mathematical physics earned him the highest Isa Singer, who also visited UC during Michael’s invaluable.