Gopal Prasad
   HOME

TheInfoList



OR:

Gopal Prasad (born 31 July 1945 in
Ghazipur Ghazipur is a city in the state of Uttar Pradesh, India. Ghazipur city is the administrative headquarters of the Ghazipur district, one of the four districts that form the Varanasi division of Uttar Pradesh. The city of Ghazipur also constitute ...
,
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
) is an Indian-American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
. His research interests span the fields of
Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...
s, their
discrete subgroup In mathematics, a topological group ''G'' is called a discrete group if there is no limit point in it (i.e., for each element in ''G'', there is a neighborhood which only contains that element). Equivalently, the group ''G'' is discrete if and o ...
s,
algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...
s,
arithmetic group In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example \mathrm_2(\Z). They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theor ...
s, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups. He is the
Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...
Professor of Mathematics at the
University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...
in
Ann Arbor Anne, alternatively spelled Ann, is a form of the Latin female given name Anna (name), Anna. This in turn is a representation of the Hebrew Hannah (given name), Hannah, which means 'favour' or 'grace'. Related names include Annie (given name), ...
.


Education

Prasad earned his bachelor's degree with honors in Mathematics from
Magadh University Magadh University is a public state university and institution of higher education in Bodhgaya, Bihar, India. It is recognised by the University Grants Commission (UGC). The university is governed by the Bihar State University Act 1976. It pro ...
in 1963. Two years later, in 1965, he received his master's degree in Mathematics from
Patna University Patna University is a public state university in Patna, Bihar, India. It was established on 1 October 1917 during the British Raj. It is the first university in Bihar and the seventh oldest university in the Indian subcontinent in the modern er ...
. After a brief stay at the
Indian Institute of Technology Kanpur The Indian Institute of Technology Kanpur (IIT Kanpur) Hindi: भारतीय प्रौद्योगिकी संस्थान कानपुर) is a public institute of technology located in Kanpur, Uttar Pradesh, India. It was ...
in their
Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
program for Mathematics, Prasad entered the Ph.D. program at the
Tata Institute of Fundamental Research Tata Institute of Fundamental Research (TIFR) is a public deemed research university located in Mumbai, India that is dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the D ...
(TIFR) in 1966. There he began a long and extensive collaboration with his advisor
M. S. Raghunathan Madabusi Santanam Raghunathan FRS is an Indian mathematician. He is currently Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly Professor of eminence at TIFR in Homi Bhabha Chair. Raghunathan receiv ...
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 The University of Mumbai is a collegiate university, collegiate, State university (India), state-owned, Public university, public research university in Mumbai. The University of Mumbai is one of the largest universities in the world. , the un ...
. 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 , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...
in Ann Arbor, where he is the
Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...
Professor Emeritus of Mathematics.


Family

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 Ila Fiete is an Indian-American physicist and computational neuroscientist as well as a Professor in the Department of Brain and Cognitive Sciences within the McGovern Institute for Brain Research at the Massachusetts Institute of Technology. Fie ...
, who is Professor of Neuroscience at MIT, and five grandchildren. Shrawan Kumar, Professor of Mathematics at the
University of North Carolina at Chapel Hill A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States ...
, Pawan Kumar, Professor of Astrophysics at the
University of Texas, Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...
and
Dipendra Prasad Dipendra Prasad (born 1960) is an Indian mathematician. He is a professor of mathematics at the Indian Institute of Technology Bombay. He is a number theorist known for his work in the areas of automorphic representations and the Gan–Gross ...
, Professor of Mathematics at the
Indian Institute of Technology, Mumbai The Indian Institute of Technology Bombay (IIT Bombay or IITB) is a public research university and technical institute in Powai, Mumbai, Maharashtra, India. It is considered as one of the best engineering universities in India and is top rank ...
, are his younger brothers.


Some contributions to mathematics

Prasad's early work was on discrete subgroups of real and p-adic semi-simple groups. He proved the " strong rigidity" of lattices in real semi-simple groups of rank 1 and also of lattices in p-adic groups, see and He then tackled group-theoretic and arithmetic questions on semi-simple algebraic groups. He proved the " strong approximation" property for simply connected semi-simple groups over global function fields Prasad determined the topological central extensions of these groups and computed the "metaplectic kernel" for isotropic groups in collaboration with
M. S. Raghunathan Madabusi Santanam Raghunathan FRS is an Indian mathematician. He is currently Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly Professor of eminence at TIFR in Homi Bhabha Chair. Raghunathan receiv ...
, see 1 2and 0 Prasad and Raghunathan have also obtained results on the Kneser-Tits problem, 3 Later, together with Andrei Rapinchuk, Prasad gave a precise computation of the metaplectic kernel for all simply connected semi-simple groups, see 4 In 1987, Prasad found a formula for the volume of S-arithmetic quotients of semi-simple groups, Using this formula and certain number theoretic and Galois-cohomological estimates,
Armand Borel Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in alg ...
and Gopal Prasad proved several finiteness theorems about arithmetic groups, 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 plane In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are not isomorphic to it. Such objects are always algebraic surfaces of general ...
s (in the theory of smooth projective complex surfaces) into 28 non-empty classes 1(see also 2and 3. 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. Prasad has worked on the representation theory of reductive p-adic groups with Allen Moy. The filtrations of parahoric subgroups, referred to as the " Moy-Prasad filtration", is widely used in
representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
and
harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...
. Moy and Prasad used these filtrations and Bruhat–Tits theory to prove the existence of "unrefined minimal K-types", to define the notion of "depth" of an irreducible
admissible representation In mathematics, admissible representations are a well-behaved class of representations used in the representation theory of reductive Lie groups and locally compact totally disconnected groups. They were introduced by Harish-Chandra. Real or comp ...
and to give a classification of representations of depth zero, see and The results and techniques introduced in these two papers enabled a series of important developments in the field. In collaboration with Andrei Rapinchuk, Prasad has studied Zariski-dense subgroups of semi-simple groups and proved the existence in such a subgroup of regular semi-simple elements with many desirable properties, 5 6 These elements have been used in the investigation of geometric and ergodic theoretic questions. Prasad and Rapinchuk introduced a new notion of "weak-commensurability" of arithmetic subgroups and determined "weak- commensurability classes" of arithmetic groups in a given semi-simple group. They used their results on weak-commensurability to obtain results on length-commensurable and isospectral arithmetic locally symmetric spaces, see 7 8and 9 Together with Jiu-Kang Yu, Prasad has studied the
fixed point set A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. Specifically, in mathematics, a fixed point of a function is an element that is mapped to itself by th ...
under the action of a finite group of automorphisms of a reductive p-adic group G on the Bruhat-Building of G, 4 In another joint work, that has been used in the geometric Langlands program, Prasad and Yu determined all the quasi-reductive group schemes over a discrete valuation ring (DVR), 5 In collaboration with
Brian Conrad Brian Conrad (born November 20, 1970) is an American mathematician and number theorist, working at Stanford University. Previously, he taught at the University of Michigan and at Columbia University. Conrad and others proved the modularity theo ...
and
Ofer Gabber Ofer Gabber (עופר גאבר; born May 16, 1958) is a mathematician working in algebraic geometry. Life In 1978 Gabber received a Ph.D. from Harvard University for the thesis ''Some theorems on Azumaya algebras,'' written under the supervi ...
, 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 Jacques Tits () (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric. Life and ...
; their research monograph 6contains all this. A second monograph 7contains 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. Prasad has developed new methods for unramified and tamely ramified descents in Bruhat-Tits theory 829]. Together with Tasho Kaletha, he has recently written a book 0on Bruhat-Tits theory which contains new proofs of several results.


Honors

Prasad has received the
Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
, the Humboldt Senior Research Award, and the Raoul Bott Professorship at the University of Michigan. He was awarded the
Shanti Swarup Bhatnagar Sir Shanti Swaroop Bhatnagar OBE, FNI, FASc, FRS, FRIC, FInstP (21 February 1894 – 1 January 1955) was an Indian colloid chemist, academic and scientific administrator. The first director-general of the Council of Scientific and Industr ...
prize (by the
Council of Scientific and Industrial Research The Council of Scientific and Industrial Research (IAST: ''vaigyanik tathā audyogik anusandhāna pariṣada''), abbreviated as CSIR, was established by the Government of India in September 1942 as an autonomous body that has emerged as the l ...
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 The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...
held in Kyoto in 1990. In 2012 he became a fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.List of Fellows of the American Mathematical Society
, retrieved 2013-05-26. He has served on the Mathematical Sciences jury of the
Infosys Prize The Infosys Prize is an annual award given to scientists, researchers, engineers and social scientists of Indian origin (not necessarily born in India) by the Infosys Science Foundation and ranks among the highest monetary awards in India to re ...
from 2011 to 2018. Prasad was the Managing Editor of the
Michigan Mathematical Journal The ''Michigan Mathematical Journal'' (established 1952) is published by the mathematics department at the University of Michigan. An important early editor for the Journal was George Piranian. Historically, the Journal has been published a small ...
for over a decade, an Associate Editor of the
Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
for six years, and is an editor of the
Asian Journal of Mathematics ''The Asian Journal of Mathematics'' is a peer-reviewed scientific journal covering all areas of pure and theoretical applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, ...
since its inception.


References

''Strong rigidity of Q-rank 1 lattices'', Inventiones Math. 21(1973), 255–286. ''Lattices in semi-simple groups over local fields'', Adv.in Math. Studies in Algebra and Number Theory, 1979, 285–356. ''Strong approximation for semi-simple groups over function fields'', Annals of Mathematics 105(1977), 553–572. ''Volumes of S-arithmetic quotients of semi-simple groups'', Publ.Math.IHES 69(1989), 91–117. ''Semi-simple groups and arithmetic subgroups'', Proc.Int.Congress of Math., Kyoto, 1990, Vol. II, 821–832. ''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. ''Values of isotropic quadratic forms at S-integral points'', Compositio Mathematica, 83 (1992), 347–372; with A.Borel. ''Unrefined minimal K-types for p-adic groups'', Inventiones Math. 116(1994), 393–408; with Allen Moy. ''Jacquet functors and unrefined minimal K-types'', Commentarii Math.Helv. 71(1996), 98–121; with Allen Moy. 0 ''On the congruence subgroup problem: Determination of the "Metaplectic Kernel"'', Inventiones Math. 71(1983), 21–42; with M.S.Raghunathan. 1 ''Topological central extensions of semi-simple groups over local fields'', Annals of Mathematics 119(1984), 143–268; with M.S.Raghunathan. 2 ''Topological central extensions of SL_1(D)'', Inventiones Math. 92(1988), 645–689; with M.S.Raghunathan. 3 ''On the Kneser-Tits problem'', Commentarii Math.Helv. 60(1985), 107–121; with M.S.Raghunathan. 4 ''Computation of the metaplectic kernel'', Publ.Math.IHES 84(1996), 91–187; with A.S.Rapinchuk. 5 ''Existence of irreducible R-regular elements in Zariski-dense subgroups'', Math.Res.Letters 10(2003), 21–32; with A.S.Rapinchuk. 6 ''Zariski-dense subgroups and transcendental number theory'', Math.Res.Letters 12(2005), 239–249; with A.S.Rapinchuk. 7 ''Weakly commensurable arithmetic groups and isospectral locally symmetric spaces'', Publ.Math.IHES 109(2009), 113–184; with A.S.Rapinchuk. 8 ''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. 9 ''On the fields generated by the lengths of closed geodesics in locally symmetric spaces, preprint; with A.S.Rapinchuk.'' 0 ''Developments on the congruence subgroup problem after the work of Bass, Milnor and Serre'', In "Collected papers of
John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...
", vol.V, AMS (2010), 307–325; with A.S.Rapinchuk. 1 ''Fake projective planes'', Inventiones Math. 168(2007), 321–370, "Addendum", ibid, 182(2010), 213–227; with Sai-Kee Yeung. 2 ''Arithmetic fake projective spaces and arithmetic fake Grassmannians'', Amer.J.Math. 131(2009), 379–407; with Sai-Kee Yeung. 3 ''Nonexistence of arithmetic fake compact hermitian symmetric spaces of type other than A_n, n<5'', J.Math.Soc.Japan; with Sai-Kee Yeung. 4 ''On finite group actions on reductive groups and buildings'', Inventiones Math. 147(2002), 545–560; with Jiu-Kang Yu. 5 ''On quasi-reductive group schemes'', J.Alg.Geom. 15(2006), 507–549; with Jiu-Kang Yu. 6 ''Pseudo-reductive groups'', second edition, New Mathematical Monographs #26, xxiv+665 pages, Cambridge University Press, 2015; with Brian Conrad and Ofer Gabber. 7 ''Classification of Pseudo-reductive groups'', Annals of Mathematics Studies #191, 245 pages, Princeton University Press, 2015; with Brian Conrad. 8 ''A new approach to unramified descent in Bruhat-Tits theory'', Amer. J. Math. vol. 142 #1 (2020), 215–253. 9 ''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. 0 ''Bruhat--Tits theory: a new approach'', Cambridge University Press, UK, 2022; with Tasho Kaletha.


External links

* {{DEFAULTSORT:Prasad, Gopal 1945 births Living people 20th-century Indian mathematicians Magadh University alumni Patna University alumni University of Mumbai alumni University of Michigan faculty People from Ghazipur Tata Institute of Fundamental Research alumni Fellows of the American Mathematical Society Scientists from Uttar Pradesh Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science