### Mathematics Colloquium

# Alexey Petukhov

### (University of Manchester)

## "Gelfand-Kirillov conjecture"

** Date: ** |
Mon, September 14, 2015 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** It is known that for a solvable Lie algebra the universal enveloping algebra U(g) is equivalent in a proper (birational) sense to an algebra of differential operators in several variables. This poses the question whether or not a similar fact holds for any Lie algebra g. This question is known as the Gelfand-Kirillov conjecture. For now it seems that for most Lie algebras the Gelfand-Kirillov conjecture is false, and in my talk I will discuss the proof of the corresponding fact which involves a reduction to positive characteristic.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*