ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

**Mathematical Colloquim **

**PROGRAM**

ODELJENJE ZA MATEMATIKU MATEMATIČKOG INSTITUTA SANU |

**PROGRAM ZA SEPTEMBAR 2016.**

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 developed 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 my talk an introduction to toric topology from the viewpoint of topology and combinatorics of polyhedral products will be given. I’ll show how toric geometry and topology work in solving classical problems and state some problems which are now opened in toric topology itself.

Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici. Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.

Zoran Petric, Odeljenje za matematiku Matematickog instituta SANU