Leonid I. Vainerman

Vainerman studied mathematics at the Taras Shevchenko National University of Kyiv and graduated in 1969. He completed his Ph.D. (Candidate of Sciences in the USSR) in 1974 at Institute of Mathematics of National Academy of Sciences of Ukraine under the direction of Myroslav Horbachuk (Gorbachuk).{{cite web| url = https://www.genealogy.math.ndsu.nodak.edu/id.php?id=129343 | title = Leonid Iosifovich Vainerman | publisher = Mathematics Genealogy Project | access-date = September 10, 2023}}{{cite journal

| last1=Vainerman | first1=Leonid I.

| last2=Gorbachuk | first2=Myroslav L.

| title=On boundary value problems for a second-order differential equation of hyperbolic type in a Hilbert space

| zbl=0318.35057

| journal=Soviet Mathematics Doklady

| volume=16

| pages=401–405

| year=1975 }} Vainerman was a professor at Taras Shevchenko National University of Kyiv{{cite journal

| author1 = Vajnerman, L. I. | author2 = Kalyuzhnyj, A. A.

| title = Quantized hypercomplex systems

| zbl = 0842.46033

| journal = Sel. Math. | volume = 13 | issue = 3 | pages = 267–281

| year = 1994}}{{cite book

| last1=Vainerman | first1=Leonid I.

| last2=Filimonova| first2=Natalya B.

| editor-first1=A. Evan

| editor-last1=Iverson

| date=July 8, 1994

| title=Algorithms for Multispectral and Hyperspectral Imagery

| chapter=Hyperspectral imagery with the application of Krawtchouk polynomials

| series=Proceedings of the SPIE

| volume=2231

| pages=148–155

| doi=10.1117/12.179775| s2cid=123625669

}} until 1992. He was a professor at International Solomon University from 1992 to 2002.{{cite web| url = https://zn.ua/EDUCATION/mezhdunarodnyy_solomonov_universitet_vozrozhdenie_evreyskoy_tsivilizatsii.html | title = International Solomon University: Renassaince of Jewish Culture | website = zn.ua | language = uk | date = October 24, 1994}}

• From 1992 to 1995, Vainerman was a visiting researcher at Pierre and Marie Curie University (Paris VI). During this appointment, he had fruitful collaborations with Michel Enock{{cite journal| last1 = Enock | first1 = Michel | last2 = Vainerman | first2 = Leonid | title = Deformation of a Kac algebra by an abelian subgroup | zbl = 0876.46042 | journal = Commun. Math. Phys. | volume = 178 | issue = 3 | pages = 571–596 | year = 1996| doi = 10.1007/BF02108816 | bibcode = 1996CMaPh.178..571E | s2cid = 119863987 | url = http://projecteuclid.org/euclid.cmp/1104286767 }} and Richard Kerner.{{cite journal | author1 = Vainerman, L. | author2 = Kerner, R. | title = On special classes of n-algebras | zbl = 0864.17002 | journal = J. Math. Phys. | volume = 37 | issue = 5 | pages = 2553–2565 | year = 1996| doi = 10.1063/1.531526 | bibcode = 1996JMP....37.2553V }}
• In 1999, Vainerman was a visiting researcher at Katholieke Universiteit Leuven, where he had a fruitful collaboration with Stefaan Vaes.
• From 1998 to 2002, Vainerman was a visiting researcher at Max Planck Institute for Mathematics in Bonn, Germany.{{cite web| url = https://www.mpim-bonn.mpg.de/preprints?year=&number=&name=Vainerman&title= | publisher = Max Planck Institute for Mathematics | title = Preprints by Leonid Vainerman | access-date = September 24, 2023}}
• From 2000 to 2002, Vainerman was a visiting professor at the University of Strasbourg in France, where he organized a prominent meeting of theoretical physicists and mathematicians. While there, he also collaborated with Dmitri Nikshych and Vladimir Turaev.{{cite journal | last1 = Nikshych | first1 = Dmitri | last2 = Turaev | first2 = Vladimir | last3 = Vainerman | first3 = Leonid | title = Invariants of knots and 3-manifolds from quantum groupoids | zbl = 1021.16026 | journal = Topology Appl. | volume = 127 | issue = 1–2 | pages = 91–123 | year = 2003| doi = 10.1016/S0166-8641(02)00055-X | s2cid = 16661718 | doi-access = free | arxiv = math/0006078 }}

Vainerman joined the University of Caen Normandy as an associate professor in Nicolas Oresme Mathematics Laboratory, becoming a full professor in 2005. He directed three Ph.D. dissertations there (those of Pierre Fima, Camille Mével and Frank Taipe).{{cite web| url = https://theses.fr/fr/085548537 | title = Leonid Vainerman | publisher = ABES search engine for French doctoral theses (theses.fr) | access-date = September 10, 2023}} He has been a professor emeritus at University of Caen Normandy since 2015. While at Caen, Vainerman collaborated with Dmitri Nikshych and Jean-Michel Vallin.

In the 1970s, Vainerman collaborated with George I. Kac (Georgii Isaakovich Kats){{cite journal

| last1=Vainerman | first1=Leonid I.

| last2=Kats| first2=George I.

| title=Nonunimodular ring groups and Hopf–von Neumann algebras

| journal=Doklady Akademii Nauk SSSR

| volume=211

| issue=5

| year=1973

| pages=1031–1034

| zbl=0296.46072

| url=https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=dan&paperid=37841&option_lang=eng}} on generalizations of Pontryagin duality to non-commutative groups and developed the concept now known as Kac algebras{{cite journal

| last1=Berezanskii | first1=Yu. M.

| last2=Berezin | first2=F. A.

| last3=Bogolyubov | first3=N. N.

| last4=Vainerman | first4=L. I.

| last5=Daletskii | first5=Yu. L.

| last6=Kirillov | first6=A. A.

| last7=Palyutkin | first7=V. G.

| last8=Khatset | first8=B. I.

| last9=Èidel'man | first9=S. D.

| title=Georgii Isaakovich Kats (obituary)

| journal=Russian Mathematical Surveys

| volume=34

| issue=2

| date=1979

| pages=213–217

| doi=10.1070/RM1979v034n02ABEH002912| bibcode=1979RuMaS..34..213B

| s2cid=250754802

}}{{cite book

| last1=Izumi | first1=Masaki

| last2=Kosaki | first2=Hideki

| title=Kac algebras arising from composition of subfactors: General theory and classification

| zbl = 1001.46040

| series=Memoirs of the American Mathematical Society

| volume=158

| date=2002

| issue=750

| doi=10.1090/memo/0750}}{{cite journal

| last1=Vainerman | first1=Leonid

| title=Ideas that will outlast us

| zbl=1302.01050

| journal=Newsletter of the European Mathematical Society

| volume=92

| pages=16–21

| year=2014

| url=https://ems.press/content/serial-issue-files/13722}}{{cite book

| last1=Masuda | first1=Toshihiko

| last2=Tomatsu | first2=Reiji

| title=Classification of actions of discrete Kac algebras on injective factors

| zbl=1376.46052

| series=Memoirs of the American Mathematical Society

| volume=245

| year=2016

| issue=1160

| doi=10.1090/memo/1160| s2cid=119321613

}} (distinct from Kac-Moody algebras).

According to the French mathematician Alain Connes,{{cite book | url = https://link.springer.com/book/10.1007/978-3-662-02813-1#about-this-book| first = Alain | last = Connes | title = Preface to the book 'Kac algebras' | year=1992 | publisher = Springer| doi = 10.1007/978-3-662-02813-1 | isbn = 978-3-642-08128-6 }} {{cquote|The theory of Kac algebras and their duality, [was] elaborated independently by M. Enock and J. -M. Schwartz, and by G. I. Kac and L. I. Vainermann in the seventies. The subject has now reached a state of maturity }}

The two teams independently developed a general Pontryagin duality theory for all locally compact groups. The contributions of both teams are covered in the 1992 book by Michel Enock and Jean-Marie Schwartz on Kac algebras.{{cite book |last1=Enock|first1=Michel|last2=Schwartz|first2=Jean-Marie|title=Kac Algebras and Duality of Locally Compact Groups|year=1992|publisher=Springer-Verlag|isbn=978-3-540-54745-7| others=With a preface by Alain Connes. With a postface by Adrian Ocneanu| location= Berlin|mr=1215933|doi=10.1007/978-3-662-02813-1}} Per Alain Connes, these results form "a general theory to characterize quantum groups among Hopf algebras, similar to the characterization of Lie groups among locally compact groups." As mentioned in the postface by {{ill|Adrian Ocneanu|de}} to the book by Enock and Schwartz, Kac algebras and their actions on von Neumann algebras naturally arise in the theory of subfactors developed by Vaughan Jones.{{cite journal

| last1=Izumi | first1=Masaki

| last2=Longo | first2=Roberto

| last3=Popa | first3=Sorin | authorlink3=Sorin Popa

| title=A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras

| zbl=0915.46051

| journal=Journal of Functional Analysis

| volume=155

| issue=1

| pages=25–63

| date=1998

| doi=10.1006/jfan.1997.3228 | doi-access=free| arxiv=funct-an/9604004

}}

In his subsequent research, Vainerman obtained results on C*-algebras, Hopf algebras and quantum groups, as well as quantum hypergroups and quantum groupoids.{{cite journal

| last1=Chapovsky | first1=Yu. A.

| last2=Vainerman | first2=L. I.

| title=Compact quantum hypergroups

| zbl=0987.81039

| journal=Journal of Operator Theory

| volume=41

| issue=2

| pages=261–289

| date=1999

| jstor=24715161

| url=https://www.theta.ro/jot/archive/1999-041-002/1999-041-002-002.pdf}}

{{cite book

| last1=Nikshych | first1=Dmitri

| last2=Vainerman | first2=Leonid

| chapter=Finite quantum groupoids and their applications

| zbl=1026.17017

| isbn=9780521815123

| editor-last=Montgomery | editor-first=Susan

| title=New directions in Hopf algebras

| publisher=Cambridge University Press

| series=Mathematical Sciences Research Institute Publications

| volume=43

| pages=211–262

| date=2002

}}{{cite journal

| last1=Vaes | first1=Stefaan

| last2=Vainerman | first2=Leonid

| title=Extensions of locally compact quantum groups and the bicrossed product construction

| zbl=1034.46068

| journal=Advances in Mathematics

| volume=175

| issue=1

| pages=1–101

| date=2003

| doi=10.1016/S0001-8708(02)00040-3 | doi-access=free| arxiv=math/0101133

}}

{{cite journal

| last1=Vainerman | first1=Leonid

| last2=Vallin | first2=Jean-Michel

| title=Classifying (weak) coideal subalgebras of weak Hopf $C^*$-algebras

| zbl=1446.16037

| journal=Journal of Algebra

| volume=550

| pages=333–357

| date=2020

| doi=10.1016/j.jalgebra.2019.12.026| doi-access=free

| arxiv=1904.07602

}}

He is credited as a co-author or editor in more than 70 mathematics publications.{{cite web | url = https://mathscinet.ams.org/mathscinet/MRAuthorID/191849 | title = Publication of Leonid I. Vainerman | publisher = MathSciNet | access-date = September 10, 2023}}{{cite web| url = https://www.researchgate.net/profile/Leonid-Vainerman | title = Leonid Vainerman | access-date = September 10, 2023}}

Vainerman organized a meeting at the University of Strasbourg February 21–23, 2002 that assembled theoretical physicists and mathematicians specializing in quantum group and quantum groupoid applications in quantum theories beyond the Standard Model. Vainerman edited the proceedings of the meeting and had them published as a book in 2003.{{cite book|editor-first=Leonid|editor-last=Vainerman|title=Locally Compact Quantum Groups and Groupoids: Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, February 21–23, 2002|series = IRMA Lectures in Mathematics and Theoretical Physics. 2 | url=https://books.google.com/books?id=0ecjM-nPhGcC|access-date=September 10, 2023|year=2003|publisher=Walter de Gruyter|isbn=978-3-11-020005-8|pages=247|zbl = 1005.00029}}

{{reflist}}

• Leonid Vainerman's [https://www.mathnet.ru/eng/person23212 mathematics publications] from 1973 to 1995 at Math-net.ru; the same list [https://www.mathnet.ru/rus/person23212 in Russian].
• Leonid Vainerman's [https://mathscinet.ams.org/mathscinet/MRAuthorID/191849 mathematics publications] at MathSciNet
• Leonid Vainerman's [https://zbmath.org/authors/?q=Leonid+Vainerman mathematics publications] at zbMATH Open
• [https://arxiv.org/search/math?searchtype=author&query=Vainerman%2C+L Preprints by Leonid Vainerman] on arXiv
• Leonid Vainerman's [https://www.researchgate.net/profile/Leonid-Vainerman publications] on ResearchGate
• [https://lmno.unicaen.fr/ Nicolas Oresme Mathematics Laboratory] at the University of Caen

{{Authority control}}

{{DEFAULTSORT:Vainerman, Leonid}}

Category:Living people

Category:1946 births

Category:Scientists from Kyiv

Category:Soviet mathematicians

Category:20th-century Ukrainian mathematicians

Category:21st-century French mathematicians

Category:Academic staff of the University of Caen Normandy

Category:Taras Shevchenko National University of Kyiv alumni

Category:Operator theorists