DEGREES:
Doctor of Sciences, Institute of Mathematics Siberian Division USSR Academy of Sciences, Novosibirsk, 1989
Ph. D., Institute of Mathematics Siberian Division USSR Academy of Sciences, Novosibirsk, 1979
M. S., Novosibirsk State University, Novosibirsk, 1974
Tel.: (617)353-2560 (math main office)
E-MAIL ADDRESS: levit@math.bu.edu
Positions Held:
Boston University 96-04, 06-present, Lecturer; Institute of Mathematics (Novosibirsk): Research Professor 1989-present, Senior Researcher 1986-1989;
Novosibirsk State University (Novosibirsk): Full Professor 1989-present, Associate Professor 1986-1989, Graduate student 1974-1977;
Samara State University (Samara, former Kuibyshev): Senior Researcher 1985-1986, Associate Professor 1979-1985, Assistant Professor 1977-1979.
MEMBER: Scientific Council on Awarding Doctor of Sciences Degree, Institute of Mathematics, 1992-present, Novosibirsk; American Mathematical Society 93-03
Research interests: Special and General Relativity, Causal Orderings in Lie Groups, Mathematical Methods in Theoretical Physics, Chronometric Theory
CONFERENCE PARTICIPATION AT:
Third International Conference on the Nature and Ontology of Spacetime, Montrel, Canada, June 13-15, 2008
X International Congress on Bioelectrography "Science, Information, Spirit", Saint Petersburg, Russia, July 7-9, 2006.
International Congress "NeuroBioTelecom-2004", Saint Petersburg, Russia, December 14-17, 2004.
International Conference on Complex Systems, "NECSI-2004", Boston, May 2004.
International Conference on "The Unity of Mathematics", Harvard University, Cambridge, MA; 2003.
JDG Fifth Conference on Geometry and Topology, Harvard University, Cambridge, MA; 2002.
NECSI International Conference on Complex Systems, Nashua, NH, 2000.
Conference on Constructive Quantum Field Theory, MIT, Cambridge, MA, 1995.
Symposium on Quanization and Nonlinear Wave Equations, MIT, Cambridge, MA, 1994.
International Conference "Invariant Ordering in Geometry and Algebra", Oberwolfach, F.R.G., 1993
II International Wigner Symposium, Goslar, F.R.G., 1991
USSR Conferences on Geometry "In the large": 1989, 1987, 1982.
III International Symposium on Group Theoretical Methods in Physics, Yurmala, Latvia, 1985
VI Soviet Gravitational Conference, Moscow, 1984
II International Symposium on Group Theoretical Methods in Physics, Zvenigorod, USSR, 1982
SOME ADDITIONAL PROFESSIONAL ACTIVITIES
Referee for Journal of Mathematical Physics. Referee for Siberian Mathematical Journal. Referee for Matemeticheskie Zametki. Reviewer for Mathematical Reviews. Referee for Archiv der Mathematik.
SOME COURSES TAUGHT (at the BU Department of Mathematics and Statistics if not otherwise specified)
Summer I 08 MA 225
Spring 08 MA 293
Fall 07 MA 118, MA 123
Summer 07 MA 120
Spring 07 MA 242 A1, MA 242 B1
Fall 06 MA 121, MA 123
Summer 06 MA 120
Spring 06 MA 118, MA 122
Fall 05 Linear Algebra and Analitic Geometry, Saint Petersburg University of Aerospace Technology, Russia
Summer 05 MA 242, MA 226
Fall 04 MA 917 (analogue of) graduate course, Saint Petersburg State University, Russia
Spring 04 MA 118, MA 122
Fall 03 MA 123, MA 129, MA 142
Summer 03 MA 225, MA 242
Spring 03 MA 118, MA 123, MET MA 123
Fall 02 MA 123, MA 127, MA 142
Summer 02 MA 225, MA 242
Spring 02 MA 118, MA 123, MET MA 120
Fall 01 MA 123, MA 118, MA 142
Summer 01 MA 225 A2, MA 225 B1
Spring 01 MA 118, MA 123, MET MA 120
Fall 00 MA 123, MET MA 123, MA 124
2000 Summer I MA 124, Summer II MA 124, MA 412
Spring 00 MA 123, MA 225, MA 118
Fall 99 MA MET 124, MA MET 123, MA 193, MA 118
Summer 99 MA 124 (Calculus II), 18.076 (at M.I.T.) Methods of Applied Mathematics
Spring 99 MET MA 124 (Calculus II), MA 225 (Calculus III)
Fall 98 MA 123 (Calculus, A1, B1, G1, S1 classes), Summer 98 MA 411 (Advanced Calc.), MA 412 (Complex Variables), Spring 98 MA 124 (Calc II), MA 242 (Linear Algebra).
Fall 97 MA 124 (Calc II), MA 717 (Functional Analysis), Summer 97 MA 242 (Linear Algebra), Summer 97 MA 411 (Advanced Calculus), Spring 97 MA 226 (Diff. Equations) Spring 97 MA 562 (Applied Mathematics II).
Fall 96 MA 225 (Multivar. Calc.), Fall 96 MA 124 (Calculus), Summer 96 Advanced Applied Mathematics, Dept. of Math., MIT.
Fall 95 MA 963, Homogeneous Differential Geometry, Informal Lecture Course.
In 1979-95 I have been teaching Geometry and Linear Algebra, Calculus I, II, III; Differential Geometry, Elements of Special and General Relativity, General Topology, Foundations of Geometry, Lorentzian Geometry, Homogeneous Spaces, Analytic Geometry, Elements of representations theory at Samara and at Novosibirsk State Universities in Russia.
SUPERVISION
Samara State University: over 10 of my students have obtained the M. S.; at Novosibirsk State University: over 10 of my students obtained M. S., one obtained a Ph. D. At the Novosibirsk Scientific Center I coordinated research of a group of mathematicians and physisists dedicated to the Chronometric Theory and its applications in theoretical physics.
LIST OF MAIN PUBLICATIONS
(the total number of publications exceeds 60)
A. TEXTBOOKS FOR STUDENTS
7. Homogeneous Spaces and Segal's Chronometry (in Russian), coursepack based on 2004 lecture course at the Department of Mathematics, Saint Petersburg State University, Saint Petersburg, Russia, 33pp, 2006. Accessible at http://www.levichev.com
6. Conformal Group Acttions in Induced Bundles (with T. Kohl and A. Glebov), Boston University, Department of Mathematics, coursepack, 18pp, 2001.
5. Homogeneous Differential Geometry (a few basic notions and examples), Boston University, Department of Mathematics, coursepack, 35pp, ISBN 1-58593-378-3, 1999.
4. Analysis in cosmic bundles (1993, with V. Yu. Levicheva), graduate textbook, Novosibirsk State University, Novosibirsk, in Russian.
3. Homogeneous chronogeometry I, 52pp. (graduate textbook, NSU, Novosibirsk, 1991), in Russian.
2. Metodicheskie ukazaniia for practical studies in tensor algebra, Kuibyshev, KSU, 8pp, for undergaduates, 1980, with A. O. Korneeva), in Russian.
1. Translation-invariant order in a vector space, Kuibyshev, KSU, 15pp. (undergraduate textbook, 1980), in Russian.
B. RESEARCH AND SURVEY ARTICLES
29. DLF-approach as the development of Segal's chronometric theory. III: More on the tachyonic component. In: Proceedings of Measuring Energy Fields (Intl. Sci. Conf.), Kamnik, Tunjice, 13-14 October 2007/ Ed. Igor Kononenko, pp.72-75
28. Representations, Chronometric Quantum Mechanics, and the DLF-modification of the Penrose-Hameroff Approach to Consciousness. In: "Science, Information, Spirit"/Proceedings of the Tenth International Congress on Bioelectrography, Saint Petersburg, Russia, 2006, pp.199-202
27. The 3-fold Way and Consciousness Studies, with K.Korotkov, 23pp. Accessible at the Moscow State University Institute of Time Exploration electronic library, May 2005, http://www.chronos.msu.ru
26. Parallelizations of Chronometric Bundles Based on the Subgroup U(2), Izvestia RAEN, ser.MMMIU, 8(2004), n.3-4, 69-79, in Russian
25. Mathematical unity of the three worlds from the "Ethics Alive' teaching. Grani Epohi, 18(2004), http://grani.agni-age.net, in Russian
24. "Russian Troika" as the New Spatio-Temporal paradigm. Electronic library of the Time Studies Seminar,2004, Moscow State University, http://www.chronos.msu
23. Three Symmetric Worlds Instead of the Minkowski Space-Time, RANS Transactions, ser.MMMIU, 7(2003), nos.3-4, 87-93
22. Certain Chronometric Bundles over Compact Worlds: Triviality of Scalar and Spinor Bundles, Siberian Advances in Mathematics, 2003, N4
21. On the Notion of Induced Representation of a Lie Algebra: Geometric Description and Chronometric Applications, "Siberian Advances in Mathematics", 2001, v.11, N4, 1-12.
20. Geometric Description of Induced Representation of a Lie Algebra, In: "Geometry and Applications"/Proceedings of the Novosibirsk Conference (March 13-16, 2000), published in Novosibirsk, Russia, p.57
19. Intervals in Space-Time: A.D.Alexandrov is 85, Reliable Computing 4(1998): 109-112, with O.Kosheleva.
18. Mathematical foundations and physical applications of Chronometry, in "Semigroups in Algebra, Geometry, and Analysis", Eds. J. Hilgert, K. Hofmann, and J. Lawson, de Gryuter Expositions in Mathematics, Berlin 1995, viii+368 pp; 77-103.
17. On the notion of induced representation, Sib. mat. Zh., 36(1995), n. 4, 857-861 (with A. N. Kuzemchikov).
16. On mathematical foundations of chronometry, Vestnik Moskovskogo Universiteta, Ser.1, Math.Mech.(1994), n. 3, 3 - 6, in Russian
15. The Chronometric Theory by I. Segal is the Crowning Accomplishement of Special Relativity, Izvestia VUZov. Fizika (1993), n. 8, 84-89 (in Russian)
14. Distinguishability condition and the future semigroup, Seminar Sophus Lie, 2(1992), 2, 205-212 (with V. Yu. Levicheva).
13. Three totally vicious homogeneous Lorentzian spaces, Siberian Advances in Mathematics, 2(1992), n. 1, 133-143.
12. Causal structure of left-invariant Lorentzian metrics on the Lie group M(2)*R(2), Sib. Math. J., 31(1990), 607-614
11. Method for Investigating the Causal Structure of Homogeneous Lorentzian Manifolds, Sib. Math. J., 31(1990), 395-408
10. The Causal Structure of an Anti-Mach Metric (with V. A. Kushmantzeva), Sib. Math. J., 31(1990), 950-955
9. A Time Machine in the MTT-World, Sib. Math. J., 33(1990), 169-171
8. On the causal structure of homogeneous Lorentzian manifolds (1989), Gen. Relat. & Grav., Vol. 21, n. 10, 1027-1045.
7. New methods for investigating the causal structure of homogeneous spaces of the relativity theory, in:"Gravitation and Fundamental Interactions",21-22 (1988, Moscow), in Russian.
6. Prescribing the conformal geometry of a Lorentzian manifold by means of its causal structure, Soviet Math. Dokl., 35(1987), 452-455
5. A left-invariant Lorentzian order on the basic affine group, Sib. Math. J., 27(1987, 473-476
4. Chronogeometry of an electromagnetic wave given by a bi-invariant metric on the oscillator group, Sib. Math. J., 27(1986), 237-245
3. Lie algebras admitting elliptic semialgebras, Funct. Anal.& Appl., 20(1986), 146-148
2. More on geometry of symmetric Lorentzian spaces, Vestnik Moskovskogo gosudarstvennogo universiteta. Ser.1, Math., Mech., 5(1986), 97, in Russian
1. On the foundations of the relativity theory (with A.Guts), in Soviet Math. Dokl., 30(1984), 253-257