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: Visiting Researcher Aug 2010 - present; Lecturer 1996-2004, 2006-Spring 2010; Institute of Mathematics (Novosibirsk): Research Professor 1989-present, Senior Researcher 1986-1989;
Novosibirsk State University (Novosibirsk): Full Professor 1989-1995, 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, 1992-2004, 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:
XII International Conference "Roerich Heritage" (RH-12), Saint Petersburg, Russia, October 9-11, 2012
XI International Conference "Roerich Heritage" (RH-11), Saint Petersburg, Russia, October 8-10, 2011
IIId All-Russian Conference "Knowledge-Ontology-Theory" (KONT-11) with international participation, Novosibirsk, Russia, October 3-5, 2011
International Scientific Conference at the Saint Petersburg State University of Arts and Culture, 11-12 February 2011, poster presentation
International Conference "Geometry and Analysis", Novosibirsk, Russia, September 14-20, 2009
Third International Conference on the Nature and Ontology of Spacetime, Montreal, 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
Arranged for and ran the DLF seminar at the Roerich Family Museum-Institute, Saint Petersburg, Russia, October 9, 2011
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)
Spring 2013 "Space, Time, Motion"
Fall 2012 "Homogeneous Chronogeometry, Part 2"
Spring 2012 "Homogeneous Chronogeometry"
Spring 2011 "Topics in Chronogeometry, Part 2" (00cwr-dlf1011)
Fall 2010 "Topics in Chronogeometry" (00cwr-dlf1011)
Spring 2010 MET MA 120 B1, MET MA 120 D1
Fall 09 MA 113, MA 120
Years 2006 - 2009: MA 123, MA 121, Algebra and Trigonometry (at Bay State College), MA 124, MA 225, MA 118, MA 123
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
Summer 99 MA 124 (Calculus II), 18.076 (at M.I.T.) Methods of Applied Mathematics
Summer 98 MA 411 (Advanced Calc.), MA 412 (Complex Variables),
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
Boston University Mentor (through BU UROP), 2010 - present
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 physicists 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
Topics in Chronogeometry, BU online course pack, 2010/2011, Available at http://math.bu.edu/people/levit
7. Homogeneous Spaces and Segal's Chronometry (in Russian), course pack based on 2004 lecture course at the Department of Mathematics, Saint Petersburg State University, Saint Petersburg, Russia, 33pp, 2006. Available at http://math.bu.edu/people/levit
6. Conformal Group Actions in Induced Bundles (with T. Kohl and A. Glebov), Boston University, Department of Mathematics, course pack, 18pp, 2001.
5. Homogeneous Differential Geometry (a few basic notions and examples), Boston University, Department of Mathematics, course pack, 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
43 (with J. Feng) More on the Mathematics of the DLF Theory: Embedding of the Oscillator World L into Segal's Compact Cosmos D. American Journal of Undergraduate Research, Vol.11, NOS 3&4, 29-33 (2012-13)
42. (with A. Akopyan) The Sviderskiy formula and a contribution to Segal's chronometry. Mathematical Structures and Modeling (2012), 25: 44-51
41. (with J. Feng) More on the mathematics of the 3-Fold Model: embedding of the oscillator world L into Segal's compact cosmos D. http://grani.agni-age.net/pdf/5013.pdf
40. (with A. Akopyan) On SO(3,3) fractional linear action on SO(3). The Fourth Geometry Meeting dedicated to the centenary of A.D.Alexandrov. Saint petersburg, Russia. Abstract (p.33) http://www.pdmi.ras.ru/EIMI/2012/A100/abstr.pdf
39. Parallelization in vector bundles as a mathematical correlate of Tulku's "focal setting" (with Louis Thiery), in Russian. XI Roerich Heritage Conference Proceedings (2011), 8-10 October, 52-53, Saint Petersburg University, Saint Petersburg, Russia.
38. Algebro-geometric transition from Special Relativity to the DLF theory. IIId "Knowledge-Ontology-Theory" Conference Proceedings (2011), 3-5 October, Vol.2, 51-58, Novosibirsk, Sobolev Institute of Mathematics of the Russian Academy of Sciences, in Russian
37. Theoretical (Sintax-Semantical) Prospects of the Kant Philosophy of Time. Philosophy of Science (2011), 2(49), 41-51 (with K. F. Samokhvalov), in Russian
36. Pseudo-Hermitian realization of the Minkowski world through DLF theory. Physica Scripta (The physics of elementary particles and fields), vol. 83 (2011), N. 1, pp.1-9.
35. Segal's chronometry: emergence of the theory and its application to physics of particles and interactions. In: The Search for Mathematical Laws of the Universe: Physical Ideas, Approaches and Concepts, eds. M.M.Lavrentiev and V.N.Samoilov (Novosibirsk: Academic Publishing House), pp. 69-99, 2010 (in Russian)
34. (with O.S.Svidersky) Lie groups U(p,q) of matrices of size p+q as a single system based on linear-fractional transformations: I. General consideration and cases p+q = 2,3. Proceedings of the International Conference "Contemporary problems in Analysis and Geometry", pp.68-69, Sobolev Institute of Mathematics SD RAS, Novosibirsk, Russia, 2009.
33. The simplest matrix realization of the oscillator Lie algebra. In: "Science, Information, Spirit"/Proceedings of the XIIIth International Congress on Bioelectrography, Saint Petersburg, Russia, 2009, pp.40-42
32. Oscillator Lie algebra and algebras u(2), u(1,1), as a single matrix system in u(2,1). In: "Lie algebras, algebraic groups, and the theory of invariants"/Proceedings of the Summer School-Conference, Samara, Russia, June 8-15 2009, pp.32-34
31. An example of a singular action of scale transformations within the linear-fractional action of the conformal group on the non-compact group U(1,1). In: "Science, Information, Spirit"/Proceedings of the XIIth International Congress on Bioelectrography, Saint Petersburg, Russia, 2008, pp.141-144
30. Contractions of certain subalgebras of the conformal Lie algebra su(2,2) in the context of the DLF-theory. (With O.S.Svidersky) In: "International Conference Dedicated to the 100th Anniversary of the Birthday of Sergei L. Sobolev", Novosibirsk, October 12-14, 2008/ p.392
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, 10 (2006), n.1-2, 51-61, 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 Accomplishment 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