The International Conference on
Secondary Calculus and Cohomological Physics,
Moscow, August 24 - August 31, 1997


The International Conference Secondary Calculus and Cohomological Physics was organized by an initiative of the Diffiety Institute of the Russian Academy of Natural Sciences (, and in collaboration with the M.V. Lomonosov Moscow State University and Istituto Italiano per gli Studi Filosofici. It became possible thanks to the financial support of

The scientific program was organized by the Scientific Committee consisting of

I. Batalin (Moscow), L. Bonora (Triest), R. Bryant (Durham, NC), M. Dubois-Violette (Orsay), M. Fliess (Paris), P. Griffiths (Princeton, NJ), M. Henneaux (Brussels), V. Kozlov (Moscow), J. Krasil'shchik (Moscow), G. Marmo (Naples), B. Sadovnikov (Moscow), J. Stasheff (Chapel Hill, NC), M. Talon (Paris), I. Tyutin (Moscow), C. Viallet (Paris), A. Vinogradov (Salerno - Moscow), B. Voronov (Moscow)

while the organizational arrangements were due to the Local Committee:

V. Kozlov (Moscow), B. Sadovnikov (Moscow), J. Krasil'shchik (Moscow), A. Samokhin (Moscow), M. Vinogradov (Moscow)

* * *

The meeting took place in August 24 - 31, 1997, at the Main Building of the Moscow State University and brought togerther over sixty participants from Europe, North America and Japan. The program included 50-minute invited lectures and 35- and 20-minute lectures and communications in a strong mixture of mathematical and physical talks (see the list below). The participants found this experiment successful and rather stimulating. Almost all invited lectures are published in the Contemporary Mathematics series of the American Mathematical Society, volume 219, 1998 (see abstracts below).

The list of invited speakers included:

M. Asorey, G. Barnich, C. Becchi, L. Bonora, F. Brandt, R. Bryant, M. Fliess, M. Henneaux, V. Kozlov, J. Krasil'shchik, A. Ibort, N. Maggiore, G. Marmo, M. Rasetti, J. Stasheff, A. Verbovetsky, C. Viallet, and A. Vinogradov (together with I. Anderson, M. Dubois-Violette, P. Griffiths, and N. Kamran, who, for various reasons, were not able to attend).

The complete list of the contributions to the Conference can be found below.


Vladimir ANDREEV (Russia), Infinite dimensional algebras connected with matrixes integrable equations.

Manuel ASOREY (Spain), Topological transitions (joint work with F. FALCETO, G. LUZÓN).

Glenn BARNICH (Belgium), Sh Lie structure of Poisson brackets in field theory.

Carlo BECCHI (Italy), BRS cohomology in topological field theory (joint work with S. GIUSTO, C. IMBIMBO).

Loriano BONORA (Italy), Review of BRST in superstring theory (joint work with C.S. CHU, M. RINALDI).

Friedemann BRANDT (Spain), Gauge covariant algebras and local BRST cohomology.

Robert BRYANT (USA), Conservation laws and the geometry of PDE.

Marco CASTRILLON (Spain), Gauge invariance on principal SU(2)-bundles (joint work with J. MUNOZ MASQUE).

Vladimir CHETVERIKOV (Russia), Symmetries of some integro-differential equations.

Alexei DAVYDOV (Russia), On some class in the Hochschild cohomology of fusion algebras.

Michel FLIESS (France), Control theory and infinite jets: applications and introductory theory (joint work with Jean LÉVINE, Philippe MARTIN, Pierre ROUCHON).

Kenji FUKAYA (Japan), Homological/homotopical algebra, topological field theory, and moduli spaces.

Yuri GLIKLICH (Russia), On stochastic evolution of a general relativistic quantum particle without conservation of energy.

Soso GOGILIDZE, Arsen KHVEDELIDZE (Russia), First integrals and Abelianization of first class constraints.

Dmitry GUREVICH (France), Differential complexes associated to the QYBE.

Marc HENNEAUX (Belgium), Consistent interactions between gauge fields: the cohomological approach.

Alberto IBORT (Spain), Equivariant Floer's cohomology.

Tatiana IVANOVA (Russia), ech cohomology and symmetries of the self-dual Yang - Mills equations.

Ol'ga IVANOVA (Russia), Reduced system of Bethe ansatz equations and geometry of the parametric surfaces (joint work with V. Andreev).

Igor KANATCHIKOV (Estonia), On the noncommutative Gerstenhaber algebra of the covariant Poisson brackets on forms in field theory.

Paul KERSTEN (the Netherlands), Super WDVV-equations and solutions in (3,2) and (3,4) dimensions (joint work with R. Martini).

Nina KHOR'KOVA (Russia), On reconstruction problem for nonlocal symmetries.

Hovhannes KHUDAVERDYAN (Russia), Odd invariant semidensity and divergence-like operators on an odd symplectic superspace (joint work with D.A. SAHAKYAN).

Valery KOZLOV, Sergei BOLOTIN (Russia), Symmetry and topology of dynamical systems.

Joseph KRASIL'SHCHIK (Russia), Cohomological background for recursion operators and Poisson structures in PDE.

Andrei KUDRYAVTSEV (Russia), On symmetries and conservation laws for the generalized Khokhlov - Zabolotskaya equations.

Ol'ga KUNAKOVSKAYA (Russia), Some functors on the category of SCr-manifolds.

Vitaly KUSHNIREVITCH (Ukraine), Differential structures in Leibniz superalgebra.

Tom LADA (USA), SH Lie structures of gauge symmetries in higher order spin theories.

Alexandre LAVRENOV (Belarus), Symmetry of the discrete models based on Askey - Wilson algebra.

Pierre LECOMTE (Belgium), Classification of modules of differential operators (joint work with Mathonet, Ulg, and Ovsienko, CPT Marseille-Luminy).

Nicola MAGGIORE (Italy), Algebraic renormalization of (massive) supersymmetric gauge theories.

Giuseppe MARMO (Italy), Cohomology in classical dynamics.

Michal MARVAN (Czech Republic), Direct computation of zero-curvature representations.

Valentin OVSIENKO (France), Exotic deformation quantization.

Michael PARINOV (Russia), One method of obtaining first integrals of Lorentz equation.

Jean-Baptiste POMET (France), Geometry for dynamic feedback in nonlinear control systems.

Alexander POPOV (Russia), Symmetries of self-dual gravity and Kodaira - Spencer deformation theory.

Mario RASETTI, Vittorio PENNA (Italy), Physics on non-Euclidean lattices (joint work with Mauro SPERA).

Pedro REAL JURADO (Spain), Homological perturbation theory and computability of the homology of commutative DGA-algebras (joint work with V. Alvarez, J.A. Armario and B. Silva).

Dmitry ROYTENBERG (USA), Lie bialgebroids and strongly homotopy Lie algebras (joint work with Alan Weinstein).

Vladimir RUBTSOV (France), Separation of variables for Hitchin systems.

Alexey SAMOKHIN (Russia), Symmetries of the equations containing a small parameter.

Valery SHEMARULIN (Russia), A direct method for solving initial-value problems.

Vladimir SOKOLOV (Russia), On integrable evolution non-Abelian equations.

Vladimir SOLOVIEV (Russia), Total divergences as a grading of the formal variational calculus.

Jim STASHEFF (USA), The (secret?) homological algebra of the Batalin - Vilkovisky complex.

Yuri TORKHOV (Russia), Higher differential forms and their applications.

Anatolii TSIRLIN (Russia), Vladimir KAZAKOV (Australia), Averaged relaxations of extremal problems.

Alexandre VERBOVETSKY (Russia), Horizontal (characteristic) cohomology and compatibility complex.

Claude VIALLET (France), On the invariants of some discrete groups.

Gaetano VILASI, Giuseppe MARMO, Alexandre VINOGRADOV (Italy), On the local structure of n-Poisson and n-Jacobi manifolds.

Alexandre VINOGRADOV (Italy), Introduction to Secondary Calculus.

Michael VINOGRADOV (Russia), n-ary Lie algebras of Poisson type (joint work with A. Vinogradov).

Alexander YAKHNO (Russia), Conservation laws and main boundary problems of plasticity (joint work with S.I. SENASHOV).

Valery YUMAGUZHIN (Russia), Conditions of reducibility of ODE's to the form y'''= 0 (joint work with V.N. Gusyatnikova).

Michael ZELIKIN (Russia), Solution to quadratic PDE as a connection on the integral Dirichlet's bundle.

Victor ZHARINOV (Russia), Secondary Operational Calculus.

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