Одељење за математику, 6. септембар 2016.

Наредни састанак Семинара биће одржан у уторак, 6. септембра 2016. у сали 301ф Математичког института САНУ са почетком у 14:15 часова.

Предавач: Ivan Limonchenko, Steklov Mathematical Institute of the RAS


Апстракт: Topological spaces with a compact torus action have been of great importance and interest in algebraic topology, complex, symplectic and algebraic geometry for several decades, motivating new theoretical constructions and providing numerous examples on which the general theory can be worked out explicitly. In their pioneering work of 1991 M. Davis and T. Januszkiewicz introduced the notion of a quasitoric manifold – a topological model for an algebraic toric manifold – as a space with a locally standard torus action whose orbit quotient is a simple polytope. Their work was intensively deveoped and expanded upon by V. Buchstaber, M. Masuda, T. Panov and N. Ray into what has become a whole new area of study, Toric Topology. Toric methods in algebraic topology are based on the notion of a moment-angle-complex and its generalization – a polyhedral product space.

In this talk, an introduction to toric topology from the viewpoint of topology and combinatorics of polyhedral products will be given. It will be showed how toric geometry and topology work in solving classical problems and some problems which are now opened in toric topology itself will be stated.