Joseph Bernstein

Joseph Bernstein (Иосиф Бернштейн, Tel Aviv University) посетил Лабораторию в июне 2012 г.

Он принял участие в международной конференции "Algebra and Geometry", посвященной 65-летию А.Г. Хованского, и выступил с докладом "Working with pseudo-differential operators without Fourier transform".

Abstract: Usually the definition of pseudo-differential operators is given in terms of Fourier transform. This definition is based on a local approximation of a manifold by a linear space.
In some geometric situations our manifold has additional geometric structures that can not be approximated by linear structures. In these cases the Fourier transform can not be used.
I will describe alternative definition of pseudo-differential operators that is formulated in more algebraic terms. It uses only very soft analysis, and in particular it does not use Fourier transform.
I hope that some generalizations of this definition would allow to extend the theory of pseudo-differential operators to more complicated geometric situations. I will describe an important example of such situation that naturally arises in representation theory of reductive groups (e.g. the group G = GL(n,R)).

С записью этого доклада можно ознакомиться в рубрике "Видеоматериалы".