Professor Alberto Minguez （University of Vienna/University of Sevilla・Number Theory） will deliver the Mathematics and Mathematical Sciences Global Special Lecture 2 as follows.
If you wish to attend, please register using the Google form below.

◆Date and Time:
April 8 (Wed): 10:00 a.m. – 12:00 p.m.

April 10 (Fri): 3:00 p.m. – 5:00 p.m.

April 13 (Mon): 10:00 a.m. – 12:00 p.m.

April 15 (Wed): 10:00 a.m. – 12:00 p.m.

April 17 (Fri): 3:00 p.m. – 5:00 p.m.

◆Venue:
Room 127, Building No. 3, Graduate School of Science

Title:The unitary dual of p-adic reductive groups

Abstract：
The classification of the unitary dual of a topological group is a problem of central importance in representation theory and harmonic analysis. Beyond its intrinsic interest, it governs the spectral decomposition of representations and provides the local constituents that appear in many global constructions in modern number theory. In this course we will study the unitary dual of p-adic reductive groups through the example of GL(n,F), where F is a p-adic field. This setting allows one to treat concrete questions while encountering most of the phenomena that arise more generally. The course will begin with a brief introduction to smooth representations of p-adic groups, including cuspidal representations, parabolic induction, and basic structural results. A central step will be the classification of all irreducible smooth representations of GL(n,F). We will then investigate which of these representations are unitary, focusing on representations obtained by normalized parabolic induction and on the analysis of complementary series and their endpoints. The aim is to obtain a concrete understanding of this example while highlighting ideas that extend to general reductive groups.

Registration:
Those who wish to attend are required to register via the Google Form.
Please access the form using the QR code or the URL below:

https:https://forms.gle/NftSFnsJJhdtVhBG6

Registration Deadline
April ３ (Fri)

✧✧Notes✧✧

Mathematics and Mathematical Sciences Global Lecture IV is a core course of the Mathematics and Mathematical Sciences Innovation Human Resource Development Program.

To receive course credit, registration through KULASIS is required.
(Course registration period for first-semester courses: April 17 (Fri) – April 20 (Mon))

Auditing is permitted even without KULASIS registration (limited to Kyoto University students).
Registration via the Google Form is still required.

For further details, including abstracts of each special lecture, please visit the program website:
https://www.math.kyoto-u.ac.jp/ja/ktgu/courses