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 (http://ecfor.rssi.ru/~diffiety/,
http://www.botik.ru/~diffiety)
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

- ISTITUTO ITALIANO PER GLI STUDI FILOSOFICI
- RUSSIAN FOUNDATION FOR BASE RESEARCH
- INTERNATIONAL CENTER FOR FUNDAMENTAL PHYSICS (Moscow)

The scientific program was organized by the Scientific Committee consisting of

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while the organizational arrangements were due to the Local Committee:

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**

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.

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**

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
SC ^{r}-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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