Stereotype dualities in Geometry


题目:Stereotype dualities in Geometry

报告人:Sergei Akbarov俄罗斯高等经济研究大学




地点:Zoom会议会议号:882 8540 7533密码:028422


摘要:The natural parallels between the four big geometric disciplines in mathematics,

- algebraic geometry,

- complex geometry,

- differential geometry,

- topology,

can be explained by the fact that these disciplines appear as a visual image when studying the very same reality with the help of different observation tools.A construction that formalizes this idea is called an envelope. This is a special kind of functor in category theory, generated by a class of morphisms chosen as the observation tools. In the case of the mentioned geometric disciplines, the common reality they reflect is the theory of topological (more precisely, stereotype) algebras, and the functors that transform this reality into the last three disciplines are respectively

- the holomorphic envelope, where the observation tools are the homomorphisms into Banach algebras,

- the smooth envelope, where the observation tools are the so called differential homomorphisms into C*-algebras with the joined self-adjoint nilpotent elements, and

- the continuous envelope, where the observation tools are the homomorphisms into C*-algebras.

Each of these functors generates, apart from the corresponding geometric discipline itself, a special kind of duality in it, which is called stereotype duality, and which generalizes the famous Pontryagin duality for locally compact Abelian groups (to some class of not necessarily commutative groups).

This leads to an intriguing picture, where it becomes possible to compare these geometries as disciplines, to find common features, differences, generalizations, new examples, and so on. In my talk I’m going to give accurate definitions and discuss some details of this picture.


Copyright (C)2023 哈尔滨工业大学数学研究院版权所有
电话:86413107      邮箱