Curriculum Vitae of ALEXANDER Yu. OLSHANSKII

Address:
Department of Mathematics
Vanderbilt University
1326 Stevenson Center
Nashville, TN 37240

Electronic addresses:
alexander.olshanskiy@vanderbilt.edu
olshan@shabol.math.msu.su

Education and degrees:
Undergraduate: Moscow State University (1963-1968, with honor) M.S. in Mathematics, 1968
Graduate: Moscow State University (1968-1970) Ph.D. in Mathematics, 1971
Doctor of Science in Mathematics (Habilitation), 1979

Positions held:
Assistant Professor of Mathematics, Moscow State University, 1970-1977
Associate Professor of Mathematics, Moscow State University, 1978-1984
Professor of Mathematics, Moscow State University, 1985-present
Centennial Professor of Mathematics, Vanderbilt University, 1999-present

Awards, grants and honors:

• Moscow Mathematical Society Prize winner, 1970
• Invited speaker, International Congress of Mathematics, 1982
• Kargapolov Prize "for outstanding contributions to group theory" , 1993
• Honorary Silver Badge, Seminar "Algebra \& Logic," Novosibirsk, 1987
• J. Miller Professorship, University of Illinois at Urbana Champaign, March-April 1995
• Russian Federation Presidential Award 1993-1996
• INTAS Award 1994-1998
• J. Soros Professorship, 1995-96 and 1998
• Russian Fund (awarded to outstanding research groups), 1996-1997
• Russian Fund (for fundamental research), 1996-1998
• NSF grant, 2000- 2003
• Russian Fund for fundamental research, 1999-2001, 2002-2004 (grant 02-01-00170)
• INTAS grant, 2000-2003
• Malcev Prize of the Russian Academy of Sciences for the series of papers in geometric and combinatorial group theory, 2000
• NSF grant, 2003-2006

Editorial Boards:
Communications in Algebra
International Journal of Algebra and Computation
Journal of Group Theory

Algebra and Discrete Mathematics

Ph.D. Students:
A. N. Fedorov, T. V. Dubrovina, G. S. Derjabina, V. S. Atabekian, S. V. Ivanov, V. S. Guba, K. I. Lossov, V. N. Obraztsov, A.M. Storozhev, Nguen Hung Shon, V. G. Mikaelian, A. A. Klyachko, Yu. S. Semenov, K. V. Mikhajlovskii, A. Vdovina, G.Z. Arjantseva , N.V.Bezverhniy , D.V.Osin, P.A.Kozhevnikov, A. E. Pankratjev.

Plenary and Invited 1-hour conference talks:

• International Congress of Mathematics, 1982
• At seven All-Union Algebra Conferences and five other All-Union Conferences , U.S.S.R. (1969-1990)
• Algebra Conference, Halle, 1986
• International Conference "Groups-St Andrews-1989" (four lectures)
• International Conference on Group Theory, Debrecen, 1990
• Fifth Congress of Vietnamese Mathematicians, 1990
• Workshop in Geometric and Combinatorial Methods in Group Theory, Edinburgh, 1993
• Group Theory Conference, Spetses, Greece, 1993
• Group Theory and Topology Workshop, Albany, NY, 1993
• Geometrical and Homological Methods in Group Theory, Durham, UK, 1994 (three lectures)
• Third International Conference in Group Theory, Pusan, Korea, 1994
• International Conference in Groups and Group Rings, Gliwice, Poland, 1994
• Conference on Generators and Relations in Groups, Cortona, Italy, 1994 (8 lectures)
• International Algebra Conference, Jerusalem, 1996
• International Conference on Modern Algebra and Its Applications, Nashville, USA, 1996
• International Conference on Geometric and Combinatorial Group Theory, Canberra, Australia, 1996
• International Conference on Group Theory, Montreal, Canada, 1996
• International Algebra Conference, St. Petersburg, 1997
• International Algebra Conference, Hong Kong, 1997
• Malcev Algebra Conference, Novosibirsk , 1997
• International Conference "Groups-St Andrews-1997" (two lectures)
• Conference on Geometric Group Theory, Mobile, AL, 1998
• Conference on Combinatorial Methods in Algebra, Fayetteville, 1998
• International Conference on Algorithmic Problems in Groups and Semigroups, Lincoln, USA, 1998
• International Conference in Group Theory, Pusan, Korea, 1998
• International Conference on Combinatorial and Computational Methods in Mathematics, Omsk, Russia, 1998
• Conference in Algebra, Moscow, 1999
• International Conference in Algebra, Hong Kong, 1999
• Wasatch Topology Conference, Park City, 1999 (two lectures)
• International Conference in Logic and applications, Novosibirsk, 2000
• International Conference in Group Theory, Edmonton, 2000
• Groups, Rings, Lie and Hopf Algebras, St.John's (Canada), 2001 (two lectures)
• International Conference in Algebra, Sumy (Ukraine), 2001 (two lectures)
• Euroconference in Algebra and Discrete Mathematics, Hattingen (Germany), 2001 (two lectures)
• Intern. Math. Conf., Kiev (Ukraine), 2002
• Intern. Conf. “Algebra – Geometry and Intersections”, Hattingen (Germany), 2002
• Intern. Conf. In Algebra, Krasnoyarsk (Russia), 2002
• Geometric Group Theory Conf., Pensacola (Florida), 2002

Colloquium and seminar talks:
During 1991-2003 I gave approximately 130 colloquium and seminar talks at various universities in the USA, U.K., Canada, China, Korea, Italy, Brazil, Australia, Germany, France, Singapore, Switzerland, Israel, and Russia.

RESEARCH:

Research interest:
Combinatorial Group Theory, Geometric Methods in Group Theory, Varieties of Groups and Rings

Summary of main results

• The description of varieties of residually finite groups (1969)
• The solution of the finite basis problem of B.H.Neumann (1969)
• The answer to Mal'cev's questions on group varieties (1970) and on operations over groups (1989)
• The classification of soluble just-non-Cross varieties of groups (1971)
• The answer to G. Higman's question (CREAM-hypothesis, 1973)
• The solution of B. Neumann's problem on characteristic subgroups of free groups (1973)
• The description of finite groups having a finite basis of quasi- identical relations (1974)
• The theorem on the existence of finite basis for identities in finite Lie rings and the classification of soluble just-non-Cross varieties of Lie rings (jointly with Yu. Bakhturin, 1975-76)
• The answer to questions of Alperin and Syskin on finite p-groups (1978)
• The solution of the problems of Tarski, Schmidt, Chernikov and Kurosh on groups with finiteness conditions (1978-82)
• The solution of the von Neumann - Day problem on amenable groups (1979)
• The answer to A.A.Markov's question on existence of countable non-topologised groups (1980)
• New shorter proof of the Novikov-Adian theorem for sufficiently large odd exponents (1982)
• The solution of Ph. Hall's problem on verbal and marginal subgroups (with I. S. Ashmanov, 1985)
• The solution of H. Neumann's problems on varieties (1985) and on linked products of groups (1992, with S. Ivanov)
• The description of subgroups of quasifinite groups ( with G. S. Derjabina, 1986)
• The generalization and strengthening of the Neumanns-Shmelkin theorem on products of group varieties (1986) and of the varieties of Lie algebras (2001, with A.L.Shmelkin)
• The introduction of "diagram of homomorphism" and its applications (1989)
• The solution of Phillips' problem on embeddings of periodic groups
• The solution of Gromov's problem on Burnside quotients of torsion free hyperbolic groups (1991) and the solution the same problem for any hyperbolic non-elementary group (with S. Ivanov, 1996)
• The proof of "genericity" of hyperbolic groups in definite statistical meaning (1992)
• Theorems on residual and SQ-properties of hyperbolic groups (1993-95)
• The description of the structure of locally finite subgroups in the free Burnside groups of large even exponents (with S. V. Ivanov, 1997)
• The solution of the Gromov realization problem for subgroup distortion (1997).
• The discription of the finite subgroups growth functions in p-groups (1999).
• The description of the groups having the word problem of type NP (with J.-C. Birget, E.Rips and M.Sapir)
• The solution of the Bass - Lubotzky problem on finitely presented quotients of hyperbolic groups, having no nontrivial finite factor-groups (2000)
• The construction of a finitely presented non-amenable group which has no non-cyclic free subgroups, solution of the Grigorchuk - Cohen problem (with M.Sapir, 2001)
• The solution of Adian’s problem of 1980 (proper free subgroups of the free Burnside groups of large odd exponents are not normal), 2003.
• The solution of Collins’ problem of 1976 on groups embeddings preserving the solvability of the conjugacy problem (with M.Sapir, submitted)

The list of my publications is here.

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