The purpose of this lecture series is to introduce the audience to basic ideas of specific areas of contemporary pure mathematics. Each lecture shall present an area: where it comes from, where it currently is, where it goes. Lectures will be given by prominent mathematicians twice a year: in the Spring and in the Autumn. Before and after each lecture we will organize reading seminars to prepare the audience for the lecture and to dig further into the topic of the lecture. With the lecturer’s consent, lectures will be recorded, slides and/or lecture notes will be provided if available.

*Upcoming lecture*

Michel Brion (Grenoble)**Title**: Around the inverse Galois problem**Time**: November 21, 2024, 14:00**Venue**: Room 301, Building A5, Institute of Mathematics, VAST

Online participation: Join Zoom Meeting

https://us06web.zoom.us/j/82927090825?pwd=sCz1LoTwwU9lBgM74B7Q1G1jytdD3m.1

Meeting ID: 829 2709 0825

Passcode: 123456

* Abstract*: The inverse Galois problem asks whether every finite group can be realized as the Galois group of some finite Galois extension of the field Q of rational numbers. This problem is still open, even if many partial results have been obtained. The lectures will present some of these results and a general approach due to Hilbert, via the construction of appropriate Galois extensions of the field of rational functions Q(t). Then we will turn to an analog of the inverse Galois problem for function fields in one variable over an algebraically closed field, where a positive answer is known. Finally, we will discuss a further analog, which asks whether every algebraic group can be realized as the automorphism group of some projective variety. Here the answer is generally negative, as shown by Lombardo and Maffei. But it is positive for linear algebraic groups, due to the work of Florence.

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Registration for participation: form

**Organizers: **Phung Ho Hai, Doan Trung Cuong,

**Scientific secretary**: Dao Van Thinh

**Scientific advisor**: Hélène Esnault

**Contact**:
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