This volume presents the first collection of articles consisting entirely of work by faculty and students of the Higher Mathematics College of the Independent University of Moscow (IUM). This unique institution was established to train elite students to become research scientists. Covered in the book are two main topics: quantum groups and low-dimensional topology. The articles were written by participants of the Feigin and Vassiliev seminars, two of the most active seminars at the IUM.

Readership

Graduate students and research mathematicians working in the subject areas.

Table of Contents

• S. M. Arkhipov -- Semi-infinite cohomology of quantum groups. II
• David Erschler -- Symmetry groups of regular polyhedra over finite fields
• B. L. Feĭgin and A. V. Odesskiĭ -- Coordinate ring of the quantum Grassmannian and intertwiners for the representations of Sklyanin algebras
• B. L. Feĭgin and A. V. Odesskiĭ -- Vector bundles on an elliptic curve and Sklyanin algebras
• M. Finkelberg, A. Kuznetsov, and I. Mirković -- The singular supports of IC sheaves on spaces of quasimaps are irreducible
• Boris Shoikhet -- Cohomology of the Lie algebras of differential operators: Lifting formulas

• P. M. Akhmetiev -- On a higher analog of the linking number of two curves
• S. S. Anisov and S. K. Lando -- Topological complexity of $T^2$-bundles over the circle
• S. K. Lando -- Tutte decomposition for graphs, weighted graphs, and symmetric matrices
• V. Turchin -- Homology isomorphism of the complex of 2-connected graphs and the graph-complex of trees
• V. A. Vassiliev -- On invariants and homology of spaces of knots in arbitrary manifolds