The Mathematical Center in Akademgorodok invites you to attend a mini-course of lectures "Centralizers in the first Weyl algebra: history, theory and open questions". It will be held on May 11–14 at 6:10 pm in room 5216 of the NSU Building #1.
The lecturer of the mini-course is Alexander B. Zheglov (Lomonosov Moscow State University).
The question of how the centralizers of elements in a Weyl algebra are structured has been asked many times in different works and in different contexts. Despite the well-developed theory of the classification of commuting ordinary differential operators, there are still many deep open questions about the description of centralizers within the framework of this theory. In particular, just a few explicit examples of commuting elements in the first Weyl algebra are known so far. In my lectures, I will tell you about the history of the issue, present the most important results about the first Weyl algebra, and then explain very recent results on centralizers in the context of the theory of commuting operators, as well as the current state of affairs and open questions for further research.