Fall 2002: Metric Spaces, MA-113

**Books**

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

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

- Quantizations and Symmetries, (to appear in Proceedings of the Abel Bicentennial Conference), 2002
- Relations and Quantizations in the category of probabilistic bundles, (in preparation, with Per Jakobsen)
- Quantizations of Differential Equations, Non-Linear Analysis, 47 (2001), p.2621-2632
- Calculus and quantizations over Hopf algebras, Acta Appl. Math., 5 (1998), p.303-352
- On quantum mechanics on manifolds, Acta Appl. Math, 57(1999), p.231-251
- 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.
- Color Calculus and Color Quantizations, Acta Appl. Math., v.41, (1995), p.193-226
- Braided differential operators and quantizations in ABC-categories, Competes Rendus Acad.Sci.,Paris,ser1,318(1994), p.857-862

Preprints:

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

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