Seminar o zakladech algebraicke geometrie (NMAG465 LS 2016-2017)

Karlin, Ctvrtek, 17.30, K3 (Matematicky Institut MFF UK)

Algebraic geometry can be thought of as an approach to solve problems in (commutative) algebra and related fields of computational complexity, representation theory, mathematical physics, number theory, etc., by systematically constructing necessary geometrical objects. E.g., we associate with a system of polynomial equations an algebraic variety in the corresponding affine space. The main philosophy is to associate appropriate geometric notions (points, sets, topology, mappings, etc.) with corresponding algebraic notions (ideals, rings, Zariski topology, morphisms, etc.) and vice versa. For example, a commutative algebra is considered as an algebra of functions on a set.

Our aims is to explain/highlight/understand the importance of the following topics:

(1) Lie groupoids, Lie algebroids and holonomy groupoid of foliations,
(2) ???
(3) Differentiable stack, Lie groupoid and Morita equivalence,
(4) Higher order contact structures on jet spaces and diffieties,
(5) Cohomology invariants of PDE,
(6) Formal geometry and characteristic classes of foliations,
(7) Partial (Bott) connection and characteristic classes of foliations,
(8) Crainic-Moerdijk approach to characteristic foliations,
(9) Grothendieck topology and Losik approach,
(10) Higher homotopy invariants of foliation,
(11) Classifying foliations,

The audience typically consists of mathematicians of various backgrounds.

Everybody is welcome to attend. There are no particular prerequisites for attending this seminar.

Anybody interested is kindly requested to write either to Hong Van Le or to Petr Somberg, who organize the seminar. The schedule (seminar room + time schedule coordinates) of the seminar will be adjusted accordingly.