Here you find some  information about me.

Who I am, where I'm from, and what I do.

 

Teaching:

Fall 2002: Metric Spaces, MA-113

 

 

 Publications:

Books

  1. Contact Geometry and Nonlinear Differential Equations, Cambridge University Press, (to appear), 2003 (with A. Kushner and V. Roubtsov)
  2. The Interplay between differential Geometry and Differential Equations, AMS Translations, Advances in Math. Sciences, Ser. 2, 167, 1995
  3. Lectures on Geometry of Differential Equations, 1, ''La Sapienza'', Rome, 1993
  4. Lectures on Geometry of Differential Equations, 2, ''La Sapienza'', Rome, 1993
  5. Basic ideas and concepts of differential geometry, Springer Verlag, (with D.V.Alexeevski and A.M.Vinogradov), 1991
  6. Geometry of jet spaces and non-linear differential equations, Gordon and Breach,(with I.S.Krasilshchik and A.M.Vinogradov), 1986
  7. Introduction into geometry of nonlinear differential equations, NAUKA Pub.,(in Russian) Moscow, (with I.S.Krasilshchik and A.M.Vinogradov), 1986

Papers

Differential Geometry and Differential Equations

  1. Linearizability of d-webs on 2-dimensional manifolds, (in preparation,  with M. Akivis and V. Goldberg)
  2. Mayer Brackets and PDEs solvability,I,  Differential Geometry and its Applications, (with Boris Kruglikov), p. 251-272, vol.17, 2002
  3. Quantizations of Differential Equations, Non-Linear Analysis, 47 (2001), p.2621-2632
  4. The Spencer Cohomologies, Kluwer Math. Encyclopedia ,2001
  5. On Equivalence of Differential equations, Acta et Commen. Univer. Tartuenis de Mathematica, 3 (1999), p.7-29, (with Boris Kruglikov).
  6. Theory of $G-$ difference equations (with P.Jakobsen), Acta Appl. Math. , 57(1999), p.165-204
  7. On quantum mechanics on manifolds, Acta Appl. Math, 57(1999), p.231-251
  8. Homogeneous geometric structures and homogeneous differential equations, AMS Translations, Advances in Math. Sci., Ser.2, v.167, (1995), p.143-164
  9. Spencer Cohomologies and Symmetry Groups (with L.Zilbergleit), Acta Appl. Math., v.41, (1995), p.227-245
  10. A realization of spinors in the Minkowski space (with L.Zilbergleit),  Izvestia Vuzov,  Mathematika, v.5, (1995)
  11. Singularities of Cauchy data, characteristics and cocharacteristics, and integral cobordisms, Differential geometry and applications, (1994), v.4, p.283-300(with A.Prastaro)
  12. Spencer cohomologies and symmetries, Mat. Zametki,(1994),v.5,N4, p.79-94(with L.Zilbergleit)
  13. Non-holonomic filtration: algebraic and geometric aspects of non-integrability, in the book ''Geometry of partial differential equations'',(ed. A.Prastaro and Th.Rassias)(1994), p.189-214(with V.Rubtsov)
  14. Spencer cohomologies of PDE invariant systems on homogeneous spaces, Russian Math. Doklady,238(1993)N5, p.544-546 (with L.Zilbergleit)
  15. Spencer cohomologies,in the book ''Geometry of partial differential equations'',(ed. A.Prastaro and Th.Rassias)(1994), p.215-252(with L.Zilbergleit)
  16. A local classification of Monge-Ampere equations, Ann. Sci. Ecole Norm. Super.,26(1993),N3, p.281-308 (with V.Rubtsov and I.Tchekalov)
  17. Differential equations on two-dimensional manifolds, Matematika, Izvestia VUZ, memorial issue dedicated to 200-years of N.Lobachevsky, 5(1992), p.43-57
  18. Connections and Singularities, Matematika, Izvestia VUZ, memorial issue dedicated to 200-years of N.Lobachevsky, 5(1992)p.25-35 (with L.Zilbergleit)
  19. Homogeneous structures on manifolds, Mat. Zametki, 52(1992),N4, p.54-68
  20. Non-holonomic filtration and Lie algebra cohomology, Mat. Zametki, 52(1992),N1, p.59-68 (with D.Gurevutch and V.Rubtsov)
  21. Duality in stable Spencer cohomologies, Lecture Notes in Math., (1992), p.43-55 (with L. Zilbergleit)
  22. Differential geometry via differential equations, Proc. of the Sophus Lie Memorial conference, Oslo(1992), ed. A.Laudal, p.271-289
  23. Filtration non-holonomee, ''grand crochets''et cohomologie, Competes Rendus Acad.Sci.,Paris,ser.1,313(1991) p.36-41 (with D.Gourevitch and V.Rubtsov)
  24. Symmetries of distributions and quadrature of ordinary differential equations, Acta Appl.Math.,24(1991) p.29-51 (with S.Duzhin)
  25. On solvability of parameter-depend Fucks equations, Mat. Zametki, 50(1991),N6, p.71-84
  26. Spectral sequences for stable Spencer cohomologies of differential equations over characteristic bundles, Soviet Math. Doklady, 310(1990)N5, p.1039-1042 (with L.Zilbergleit)
  27. Spencer cohomologies of differential equations, Lecture Notes in Math., v.1453(1990), p.121-136 (with L.Zilbergleit)
  28. Duality in Spencer cohomology, in Algebraic aspects of analysis and topology, Voronozh,1990, p.18-29 (with L.Zilbergleit)
  29. Non holonomic integrals of differential equations,in Differential geometry and its applications, Brno(1990), ed. D.Krupka, p.355-360 (with Yu.Romanovsky)
  30. Classification of intransitive Lie algebra actions, Matematika, Izvestiya VUZ,5(1989), p.18-26
  31. Topological indexes of Spencer complexes associated with geometrical structures, Mat.Zametki,45(1989),N4, p.59-68 (with V.Rubtsov)
  32. Geometrical theory of singularities of solutions of non-linear partial differential equations. Itogi Nauki i Tekniki, Ser. Problems of Geometry, VINITI, v.20 (1988), p.207-247
  33. Spencer cohomologies of differential equations, in Global analysis and non-linear differential equations,Voronezh,(1988), p.76-91  (with L.Zilbergleit)
  34. Singularities of solutions, spectral sequences and normal forms of Lie algebras of vector fields, Proc. of Acad. Sci. USSR, v.51 (1987), N3, p.484-511
  35. Topological aspects of geometrical theory of nonlinear differential equations, Lecture Notes in Math.,1214(1986), p.101-116
  36. Singularities of multivalued solutions of nonlinear partial differential equations, and nonlinear phenomena, Acta Appl. Math.v.3,  N2(1985), p.135-173
  37. Differential operators in fibered spaces, Uspeshi Math. Nauk, 40(1985),N2, p.187-188
  38. On micro local structure of pseudo differential operators, Math. Zbornik, 128(1985), N4, p.516-529 (with B.Sternin)
  39. Topological aspects of PDE geometrical theory, in Applications of Topology in Modern Analyses, Voronesh (1985), p.106-136
  40. On the Sophus Lie theorems for Monge-Ampere equations, Belorussian Acad. Sci. Doklady, 27(1983), N5, p.396-398(with V.Rubtsov)
  41. Spectral sequences and normal forms of Lie algebras of vector fields, Uspeshi Math. Nauk, 37(1983), N5, p.199-200
  42. Characteristic classes of solutions of differential equations, Soviet Math. Doklady, 271(1983), N6, p.1320-1324
  43. Local classification of Monge-Ampere equations, Soviet Math. Doklady, 272(1983), N1, p.34-38 (with V.Rubtsov)
  44. Geometry and topology of shock waves, Soviet Math. Doklady, 264(1982), N3, p.551-555
  45. Geometrical singularities of solutions of nonlinear differential equations, Soviet Math. Doklady, 261(1981), N6, p.1299-1303
  46. A construction of control system with distributed parameters providing invariant regimes, Cybernetics and Computer Sc. 51(1981),N51, p.36-42
  47. Singularities of solutions of differential equations, Soviet Math. Doklady, 251(1980),N4, p.794-799
  48. Contact geometry and nonlinear partial differential equations of the second order, Soviet Math. Doklady, 238(1978),N5, p.273-276
  49. On the sufficient orbits of the contact diffeomorphisms group, Math. Zbornik, 104(1977), N2, p.148-170
  50. Local classification of nonlinear partial differential equations of the first order, Uspeshi Mat. Nauk, 30(1975),N1, p.101-171
  51. Local classification of nonlinear partial differential equations of the first order, Soviet Math. Doklady, 210(1973), N3

 Quantum Mathematics:

  1. Quantizations and Symmetries,  (to appear in Proceedings of the Abel Bicentennial Conference), 2002
  2. Relations and Quantizations in the category of probabilistic bundles, (in preparation, with Per Jakobsen)
  3. Quantizations of Differential Equations, Non-Linear Analysis, 47 (2001), p.2621-2632
  4. Calculus and quantizations over Hopf algebras, Acta Appl. Math., 5 (1998), p.303-352
  5. On quantum mechanics on manifolds, Acta Appl. Math, 57(1999), p.231-251
  6. Products and quantizations in $K$-theory of braiding-commutative algebras, (with A. Prasolov), In algebraic $K$-theory and its applications, ed. H.Bass, A.Kuku, C.Pedrini, p.450-489, 1999.
  7. Color Calculus and Color Quantizations,  Acta  Appl. Math., v.41, (1995), p.193-226
  8. Braided differential operators and quantizations in ABC-categories, Competes Rendus Acad.Sci.,Paris,ser1,318(1994), p.857-862

 

Preprints:   

  1. Linearizability of d-webs on 2-dimensional manifolds, ( with M. Akivis and V. Goldberg), 2002, 17p., arXiv:mathDG/0209290
  2. Mayer Brackets and solvability PDEs,  Preprint 2001-42, Tromso University, Mars, 2001 (with Boris Kruglikov)
  3. The categorical theory of relations and quantizations, arXiv math. QA/0110311 (with P.Jakobsen), p. 1-81, 2002
  4. On equivalence of differential equations (with Boris Kruglikov), Preprint , Tromso University, Apr. 1999
  5. Symmetries and non- linear phenomena, II. Applications to nonlinear acoustics (with P.Jakobsen and Y.Romanovsky), Preprint , Tromso University, Nov. 1998.
  6. Symmetries and non linear phenomena, I (with P.Jakobsen and Y.Romanovsky), Preprint , Tromso University, 1997
  7. Theory of $G-$ difference equations (with P.Jakobsen), Preprint , Tromso University, 1997
  8. Spinors in the Minkovski space (with L.Zilbergleit) Preprint N15, Inst. of Math, University of Oslo,(1995)
  9. Color calculus and color quantizations, Preprint N3, Inst. of Math, University of Oslo,(1994)
  10. Symmetries of ordinary differential equations (with S. Moskaluk and Y. Romanovsky), Preprint ITF-94-27P, Institute of Theoretical Physics, Kiev, 1994
  11. Model differential equations (with S. Moskaluk and Y. Romanovsky), Preprint ITF-94-26P, Institute of Theoretical Physics, Kiev, 1994
  12. On $1$-st integrals of ordinary differential equations (with S. Moskaluk and Y. Romanovsky), Preprint ITF-94-25P, Institute of Theoretical Physics, Kiev, 1994
  13. Non-holonomic filtrations: algebraic and geometric aspects of integrability,Preprint IHES,M9/92(1992)(with V.Rubtsov)
  14. Symmetries and Integrals, Preprint N15, Inst. of Math, University of Oslo,(1993)(with B.Komrakov)
  15. Homogeneous geometric structures and homogeneous differential equations, Preprint IHES, M92,June-July,(1992)
  16. On a method of order decreasing for PDE, VINITI, N1734-B89 (with Yu.Romanovsky)
  17. A classification of Monge-Ampere equations. Reports of Math. Dep. Stockholm, 10(1988) (with V.Rubtsov and I.Tchecalov)
  18. Products and quantizations in $K$-theory of braiding-commutative algebras (with A.Prasolov), Preprint , Tromso University, 1997
  19. Braidings and quantizations over bialgebras, Preprint ESI N61, (1993), Wien
  20. Quantizations of differential equations, Preprint N44, Inst. of Math, University of Oslo,(1993)
  21. Quantizations of braided differential operators, Preprint ESI N51, (1993), Wien
  22. What do we need to build up quantum mechanics on manifolds? Preprint N5, Inst. of Math, University of Oslo,(1996)
  23. Calculus and quantizations over Hopf algebras ,Preprint N16, Inst. of Math, University of Oslo,(1994)

 


 

How to Reach Me

Valentin Lychagin

Institute of Mathematics and Statistics
University of Tromsø
N-9037, Tromsø
Norway


 

 Valentin Lychagin