Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object...

Biomedical engineering and medical informatics are challenging and rapidly growing areas. Applications of information technology in these areas are of paramount imp- tance. The aim of the first ITBAM conference was to bring together scientists, - searchers and practitioners from different disciplines (mathematics, bioinformatics, biology, medicine, biomedical engineering and computer science) having such c- mon interests. We hope that ITBAM conferences will provide opportunities for fru- ful discussions between all attendees and provide a platform where participants can exchange their most...

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object...

An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob- lems, whose investigation reduces, as a rule, to the study of singular integral equa- tions, where the Fredholm alternative is violated for these problems. Thanks to de- velopments in the theory of one-dimensional singular integral equations 28, 29], boundary problems for elliptic equations with two independent variables have been completely studied at...

The homology of analytic sheaves is a natural apparatus in the theory of duality on complex spaces. The corresponding apparatus in algebraic geometry was developed by Grothendieck in the fifties. In complex ana lytic geometry the apparatus of homology was missing until recently, and in its stead the hypercohomology of complex sheaves (the hyper-Ext func tors) and the Aleksandrov-Cech homology with coefficients in co presheaves were used. The homology of analytic sheaves, sheaves of germs of homology and homology groups of analytic sheaves, were intro duced and studied in the mid-seventies in...

There is no question that the cohomology of infinite- dimensional Lie algebras deserves a brief and separate mono- graph. This subject is not cover d by any of the tradition- al branches of mathematics and is characterized by relative- ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo- rems, which usually allow one to...