Russian mathematician (1937–2023)
Yuri Ivanovich Manin (Russian: Ю́рий Ива́нович Ма́нин ; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in
algebraic geometry and
diophantine geometry , and many expository works ranging from
mathematical logic to
theoretical physics .
Life and career
Manin was born on 16 February 1937 in
Simferopol , Crimean ASSR, Soviet Union.
[2]
He received a doctorate in 1960 at the
Steklov Mathematics Institute as a student of
Igor Shafarevich . He became a professor at the
Max-Planck-Institut für Mathematik in
Bonn , where he was director from 1992 to 2005 and then director emeritus.
[3]
[2] He was also a professor
emeritus at
Northwestern University .
[4]
He had over the years more than 40 doctoral students, including
Vladimir Berkovich ,
Mariusz Wodzicki ,
Alexander Beilinson ,
Ivan Cherednik ,
Alexei Skorobogatov ,
Vladimir Drinfeld ,
Mikhail Kapranov ,
Vyacheslav Shokurov ,
Ralph Kaufmann ,
Arend Bayer ,
Victor Kolyvagin and
Hà Huy Khoái .
[5]
Manin died on 7 January 2023.
[2]
Research
Manin's early work included papers on the arithmetic and
formal groups of
abelian varieties , the
Mordell conjecture in the
function field case, and
algebraic differential equations . The
Gauss–Manin connection is a basic ingredient of the study of
cohomology in families of
algebraic varieties .
[6]
[7]
He developed the
Manin obstruction , indicating the role of the
Brauer group in accounting for obstructions to the
Hasse principle via
Grothendieck 's theory of global
Azumaya algebras , setting off a generation of further work.
[8]
[9]
Manin pioneered the field of
arithmetic topology (along with
John Tate ,
David Mumford ,
Michael Artin , and
Barry Mazur ).
[10] He also formulated the
Manin conjecture , which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties.
[11]
In mathematical physics, Manin wrote on
Yang–Mills theory ,
quantum information , and
mirror symmetry .
[12]
[13] He was one of the first to propose the idea of a
quantum computer in
1980 with his book Computable and Uncomputable .
[14]
He wrote a book on
cubic surfaces and
cubic forms , showing how to apply both classical and contemporary methods of algebraic geometry, as well as
nonassociative algebra .
[15]
Awards
He was awarded the
Brouwer Medal in 1987, the first
Nemmers Prize in Mathematics in 1994, the
Schock Prize of the
Royal Swedish Academy of Sciences in 1999, the
Cantor Medal of the
German Mathematical Society in 2002, the
King Faisal International Prize in 2002, and the
Bolyai Prize of the
Hungarian Academy of Sciences in 2010.
[2]
In 1990, he became a foreign member of the
Royal Netherlands Academy of Arts and Sciences .
[16] He was a member of eight other academies of science and was also an honorary member of the
London Mathematical Society .
[2]
Selected works
Mathematics as metaphor – selected essays . American Mathematical Society. 2009.
"Rational points of algebraic curves over function fields" . AMS translations 1966 (Mordell conjecture for function fields) .
Manin, Yu I. (1965).
"Algebraic topology of algebraic varieties" . Russian Mathematical Surveys . 20 (6): 183–192.
Bibcode :
1965RuMaS..20..183M .
doi :
10.1070/RM1965v020n06ABEH001192 .
S2CID
250895773 .
Frobenius manifolds, quantum cohomology, and moduli spaces . American Mathematical Society. 1999.
[17]
Quantum groups and non commutative geometry . Montreal: Centre de Recherches Mathématiques. 1988.
Topics in non-commutative geometry . Princeton University Press. 1991.
ISBN
9780691635781 .
[18]
Gauge field theory and complex geometry . Grundlehren der mathematischen Wissenschaften. Springer. 1988.
[19]
Cubic forms - algebra, geometry, arithmetics . North Holland. 1986.
A course in mathematical logic . Springer. 1977. ,
[20] second expanded edition with new chapters by the author and
Boris Zilber , Springer 2010.
Computable and Uncomputable . Moscow. 1980.{{
cite book }}
: CS1 maint: location missing publisher (
link )
[14]
Mathematics and physics . Birkhäuser. 1981.
Manin, Yu. I. (1984).
"New dimensions in geometry" . Arbeitstagung . Lectures Notes in Mathematics. Vol. 1111. Bonn: Springer. pp. 59–101.
doi :
10.1007/BFb0084585 .
ISBN
978-3-540-15195-1 .
Manin, Yuri;
Kostrikin, Alexei I. (1989). Linear algebra and geometry . London, England: Gordon and Breach.
doi :
10.1201/9781466593480 .
ISBN
9780429073816 .
S2CID
124713118 .
Manin, Yuri; Gelfand, Sergei (1994).
Homological algebra . Encyclopedia of Mathematical Sciences. Springer.
Manin, Yuri; Gelfand, Sergei Gelfand (1996).
Methods of Homological algebra . Springer Monographs in Mathematics. Springer.
doi :
10.1007/978-3-662-12492-5 .
ISBN
978-3-642-07813-2 .
Manin, Yuri; Kobzarev, Igor (1989).
Elementary Particles: mathematics, physics and philosophy . Dordrecht: Kluwer.
Manin, Yuri; Panchishkin, Alexei A. (1995).
Introduction to Number theory . Springer.
Manin, Yuri I. (2001).
"Moduli, Motives, Mirrors" . European Congress of Mathematics . Progress in Mathematics. Barcelona. pp. 53–73.
doi :
10.1007/978-3-0348-8268-2_4 .
hdl :
21.11116/0000-0004-357E-4 .
ISBN
978-3-0348-9497-5 . {{
cite book }}
: CS1 maint: location missing publisher (
link )
Classical computing, quantum computing and Shor´s factoring algorithm (PDF) . Bourbaki Seminar. 1999. {{
cite book }}
: CS1 maint: location missing publisher (
link )
Rademacher, Hans; Toeplitz, Otto (2002).
Von Zahlen und Figuren [From Numbers and Figures ] (in German).
doi :
10.1007/978-3-662-36239-6 .
ISBN
978-3-662-35411-7 .
Manin, Yuri;
Marcolli, Matilde (2002).
"Holography principle and arithmetic of algebraic curves" . Advances in Theoretical and Mathematical Physics . 5 (3). Max-Planck-Institut für Mathematik, Bonn: International Press: 617–650.
arXiv :
hep-th/0201036 .
doi :
10.4310/ATMP.2001.v5.n3.a6 .
S2CID
25731842 .
Manin, Yu. I. (December 1991).
"Three-dimensional hyperbolic geometry as ∞-adic Arakelov geometry" . Inventiones Mathematicae . 104 (1): 223–243.
Bibcode :
1991InMat.104..223M .
doi :
10.1007/BF01245074 .
S2CID
121350567 .
Mathematik, Kunst und Zivilisation [Mathematics, Art and Civilisation ]. Die weltweit besten mathematischen Artikel im 21. Jahrhundert. Vol. 3. e-enterprise. 2014.
ISBN
978-3-945059-15-9 .
See also
References
^ Fedor Bogomolov; Yuri Tschinkel, eds. (December 2023).
"Memorial Article for Yuri Manin" (PDF) .
Notices of the American Mathematical Society . 70 (11): 1831–1849.
doi :
10.1090/noti2814 .
^
a
b
c
d
e
"Max Planck Institute for Mathematics in Bonn Mourns Death of Yuri Manin" .
Max Planck Institute for Mathematics . 8 January 2023. Retrieved 8 January 2023 .
^
"Yuri Manin | Max Planck Institute for Mathematics" . www.mpim-bonn.mpg.de . Retrieved 6 August 2018 .
^
"Emeriti Faculty: Department of Mathematics – Northwestern University" . math.northwestern.edu . Retrieved 6 August 2018 .
^
Yuri Manin at the
Mathematics Genealogy Project
^
Manin, Ju. I. (1958),
"Algebraic curves over fields with differentiation" , Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian), 22 : 737–756,
MR
0103889 English translation in Manin, Ju. I. (1964) [1958], "Algebraic curves over fields with differentiation",
American Mathematical Society translations: 22 papers on algebra, number theory and differential geometry , vol. 37, Providence, R.I.:
American Mathematical Society , pp. 59–78,
ISBN
978-0-8218-1737-7 ,
MR
0103889
^
"Gauss-Manin connection" ,
Encyclopedia of Mathematics ,
EMS Press , 2001 [1994]
^
Serge Lang (1997). Survey of Diophantine geometry .
Springer-Verlag . pp. 250–258.
ISBN
3-540-61223-8 .
Zbl
0869.11051 .
^ Alexei N. Skorobogatov (1999). "Beyond the Manin obstruction".
Inventiones Mathematicae . 135 (2). Appendix A by S. Siksek: 4-descent: 399–424.
arXiv :
alg-geom/9711006 .
Bibcode :
1999InMat.135..399S .
doi :
10.1007/s002220050291 .
S2CID
14285244 .
Zbl
0951.14013 .
^ Morishita, Masanori (2012). "Introduction". Knots and Primes . Universitext. London:
Springer . pp. 1–7.
doi :
10.1007/978-1-4471-2158-9_1 .
ISBN
978-1-4471-2157-2 .
^
Franke, J.;
Manin, Y. I. ; Tschinkel, Y. (1989). "Rational points of bounded height on Fano varieties".
Inventiones Mathematicae . 95 (2): 421–435.
Bibcode :
1989InMat..95..421F .
doi :
10.1007/bf01393904 .
MR
0974910 .
S2CID
121044839 .
Zbl
0674.14012 .
^
Atiyah, Michael ;
Drinfeld, Vladimir ;
Hitchin, Nigel ; Manin, Yuri (1978). "Construction of instantons".
Physics Letters A . 65 (3): 185–187.
Bibcode :
1978PhLA...65..185A .
doi :
10.1016/0375-9601(78)90141-X .
^ Devchand, Chandrashekar; Ogievetsky, Victor I. (1996). "Integrability of N=3 super Yang-Mills equations". Topics in statistical and theoretical physics . Amer. Math. Soc. Transl. Ser. 2. Vol. 177. Providence, RI:
American Mathematical Society . pp. 51–58.
^
a
b Manin, Yu. I. (1980).
Vychislimoe i nevychislimoe [Computable and Noncomputable ] (in Russian). Sov.Radio. pp. 13–15. Archived from
the original on 10 May 2013. Retrieved 4 March 2013 .
^ Manin:
Cubic forms – algebra, geometry, arithmetics , North Holland 1986
^
"Y.I. Manin" . Royal Netherlands Academy of Arts and Sciences. Retrieved 19 July 2015 .
^ Getzler, Ezra (2001).
"Review: Frobenius manifolds, quantum cohomology, and moduli spaces by Yuri I. Manin" .
Bull. Amer. Math. Soc. (N.S.) . 38 (1): 101–108.
doi :
10.1090/S0273-0979-00-00888-0 .
^ Penkov, Ivan (1993).
"Review: Topics in non-commutative geometry by Yuri I. Manin" . Bull. Amer. Math. Soc. (N.S.) . 29 (1): 106–111.
doi :
10.1090/S0273-0979-1993-00391-4 .
^
LeBrun, Claude (1989).
"Review: Gauge field theory and complex geometry by Yuri I. Manin; trans. by N. Koblitz and J. R. King" . Bull. Amer. Math. Soc. (N.S.) . 21 (1): 192–196.
doi :
10.1090/S0273-0979-1989-15816-3 .
^ Shoenfield, J. R. (1979).
"Review: A course in mathematical logic by Yu. I Manin" (PDF) . Bull. Amer. Math. Soc. (N.S.) . 1 (3): 539–541.
doi :
10.1090/s0273-0979-1979-14613-5 .
Further reading
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