Anton Ayzenberg, Higher School of Economics
Taras Panov, Lomonosov Moscow State University
Alexander Gaifullin, Skolkovo Institute of Science and Technology & Steklov Mathematical Institute of RAS
Omega Sirius Hotel, 'Turin' conference-hall
Toric topology is the study of topological spaces with well-behaved toric symmetries. The subject was first identified 20 years ago and has developed rapidly, with remarkably varied input from cobordism and homotopy theory, algebraic and combinatorial geometry, commutative algebra, and symplectic geometry, and integrable systems. Central objects are quasitoric manifolds and torus manifolds (topological generalizations of toric varieties), moment angle manifolds, and moment angle complexes.
Torus manifolds are often algebraic or symplectic but need not be, instead, having more flexibility in terms of studying topological and combinatorial properties. In particular, these properties give valuable information about the topology of toric varieties themselves. Moment angle complexes provide powerful links between homotopy theory, theory of space arrangements, the construction of symplectic reduction, Coxeter and Artin groups, and hyperbolic geometry.
Recently, there is a strong interest in the generalization of torus manifolds: methods of toric topology proved useful in the study of torus actions of positive complexity, such as the torus actions on Grassmann manifolds and flag manifolds. This variety of mathematical disciplines related to the subject explains the attractiveness of toric topology for young researchers. Many problems in this field are accessible for students, yet their solution has a certain interest in theoretical mathematics.
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