Gopal Prasad

[30]. Bruhat--Tits theory: a new approach, Cambridge University Press, UK, 2022; with Tasho Kaletha.

[28]. A new approach to unramified descent in Bruhat-Tits theory, Amer. J. Math. vol. 142 #1 (2020), 215–253.

[29]. Finite group actions on reductive groups and buildings and tamely-ramified descent in Bruhat-Tits theory, Amer. J. Math. vol. 142 #4 (2020), 1239–1267.

[26]. Pseudo-reductive groups, second edition, New Mathematical Monographs #26, xxiv+665 pages, Cambridge University Press, 2015; with Brian Conrad and Ofer Gabber.

[27]. Classification of Pseudo-reductive groups, Annals of Mathematics Studies #191, 245 pages, Princeton University Press, 2015; with Brian Conrad.

In collaboration with Brian Conrad and Ofer Gabber, Prasad has studied the structure of pseudo-reductive groups, and also provided proofs of the conjugacy theorems for general smooth connected linear algebraic groups, announced without detailed proofs by Armand Borel and Jacques Tits; their research monograph [26] contains all this. A second monograph [27] contains a complete classification of pseudo-reductive groups, including a Tits-style classification and also many interesting examples. The classification of pseudo-reductive groups already has many applications. There was a Bourbaki seminar in March 2010 on the work of Tits, Conrad-Gabber-Prasad on pseudo-reductive groups.

[18]. Local-global principles for embedding of fields with involution into simple algebras with involution, Commentarii Math.Helv. 85(2010), 583–645; with A.S.Rapinchuk.

[20]. Developments on the congruence subgroup problem after the work of Bass, Milnor and Serre, In "Collected papers of John Milnor", vol.V, AMS (2010), 307–325; with A.S.Rapinchuk.

[17]. Weakly commensurable arithmetic groups and isospectral locally symmetric spaces, Publ.Math.IHES 109(2009), 113–184; with A.S.Rapinchuk.

[22]. Arithmetic fake projective spaces and arithmetic fake Grassmannians, Amer.J.Math. 131(2009), 379–407; with Sai-Kee Yeung.

[21]. Fake projective planes, Inventiones Math. 168(2007), 321–370, "Addendum", ibid, 182(2010), 213–227; with Sai-Kee Yeung.

[25]. On quasi-reductive group schemes, J.Alg.Geom. 15(2006), 507–549; with Jiu-Kang Yu.

[16]. Zariski-dense subgroups and transcendental number theory, Math.Res.Letters 12(2005), 239–249; with A.S.Rapinchuk.

[15]. Existence of irreducible R-regular elements in Zariski-dense subgroups, Math.Res.Letters 10(2003), 21–32; with A.S.Rapinchuk.

[24]. On finite group actions on reductive groups and buildings, Inventiones Math. 147(2002), 545–560; with Jiu-Kang Yu.

[9]. Jacquet functors and unrefined minimal K-types, Commentarii Math.Helv. 71(1996), 98–121; with Allen Moy.

[14]. Computation of the metaplectic kernel, Publ.Math.IHES 84(1996), 91–187; with A.S.Rapinchuk.

[8]. Unrefined minimal K-types for p-adic groups, Inventiones Math. 116(1994), 393–408; with Allen Moy.

[7]. Values of isotropic quadratic forms at S-integral points, Compositio Mathematica, 83 (1992), 347–372; with A.Borel.

Prasad has received the Guggenheim Fellowship, the Humboldt Senior Research Award, and the Raoul Bott Professorship at the University of Michigan. He was awarded the Shanti Swarup Bhatnagar prize (by the Council of Scientific and Industrial Research of the Government of India). He has received Fellowships in the Indian National Science Academy, the Indian Academy of Sciences. Prasad gave an invited talk in the International Congress of Mathematicians held in Kyoto in 1990. In 2012 he became a fellow of the American Mathematical Society. He has served on the Mathematical Sciences jury of the Infosys Prize from 2011 to 2018.

[5]. Semi-simple groups and arithmetic subgroups, Proc.Int.Congress of Math., Kyoto, 1990, Vol. II, 821–832.

[4]. Volumes of S-arithmetic quotients of semi-simple groups, Publ.Math.IHES 69(1989), 91–117.

[6]. Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups, Publ.Math.IHES 69(1989), 119–171; Addendum: ibid, 71(1990); with A.Borel.

[12]. Topological central extensions of SL_1(D), Inventiones Math. 92(1988), 645–689; with M.S.Raghunathan.

In 1987, Prasad found a formula for the volume of S-arithmetic quotients of semi-simple groups, [4]. Using this formula and certain number theoretic and Galois-cohomological estimates, Armand Borel and Gopal Prasad proved several finiteness theorems about arithmetic groups, [6]. The volume formula, together with number-theoretic and Bruhat-Tits theoretic considerations led to a classification, by Gopal Prasad and Sai-Kee Yeung, of fake projective planes (in the theory of smooth projective complex surfaces) into 28 non-empty classes [21] (see also [22] and [23]). This classification, together with computations by Donald Cartwright and Tim Steger, has led to a complete list of fake projective planes. This list consists of exactly 50 fake projective planes, up to isometry (distributed among the 28 classes). This work was the subject of a talk in the Bourbaki seminar.

[13]. On the Kneser-Tits problem, Commentarii Math.Helv. 60(1985), 107–121; with M.S.Raghunathan.

[11]. Topological central extensions of semi-simple groups over local fields, Annals of Mathematics 119(1984), 143–268; with M.S.Raghunathan.

[10]. On the congruence subgroup problem: Determination of the "Metaplectic Kernel", Inventiones Math. 71(1983), 21–42; with M.S.Raghunathan.

[2]. Lattices in semi-simple groups over local fields, Adv.in Math. Studies in Algebra and Number Theory, 1979, 285–356.

[3]. Strong approximation for semi-simple groups over function fields, Annals of Mathematics 105(1977), 553–572.

[1]. Strong rigidity of Q-rank 1 lattices, Inventiones Math. 21(1973), 255–286.

Gopal Prasad's parents were Ram Krishna Prasad and Lakshmi Devi. Ram Krishna Prasad was a social worker, philanthropist, and was jailed by the British for his participation in the Indian freedom struggle against British rule. The family was involved in retail, and wholesale businesses. In 1969, he married Indu Devi (née Poddar) of Deoria. Gopal Prasad and Indu Devi have a son, Anoop Prasad, who is managing director at D.E. Shaw & Co, and a daughter, Ila Fiete, who is Professor of Neuroscience at MIT, and five grandchildren. Shrawan Kumar, Professor of Mathematics at the University of North Carolina at Chapel Hill, Pawan Kumar, Professor of Astrophysics at the University of Texas, Austin and Dipendra Prasad, Professor of Mathematics at the Indian Institute of Technology, Mumbai, are his younger brothers.

Prasad earned his bachelor's degree with honors in Mathematics from Magadh University in 1963. Two years later, in 1965, he received his master's degree in Mathematics from Patna University. After a brief stay at the Indian Institute of Technology Kanpur in their Ph.D. program for Mathematics, Prasad entered the Ph.D. program at the Tata Institute of Fundamental Research (TIFR) in 1966. There he began a long and extensive collaboration with his advisor M. S. Raghunathan on several topics including the study of lattices in semi-simple Lie groups and the congruence subgroup problem. In 1976, Prasad received his Ph.D. from the University of Mumbai. Prasad became an associate professor at TIFR in 1979, and a professor in 1984. In 1992 he left TIFR to join the faculty at the University of Michigan in Ann Arbor, where he is the Raoul Bott Professor Emeritus of Mathematics.

Gopal Prasad (born 31 July 1945 in Ghazipur, India) is an Indian-American mathematician. His research interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups.