Mathematisches Institut der Universität Bonn

Seminar on Quadratic Forms - Winter Term 2020/21

Dr. Andreas Mihatsch
Endenicher Allee 60 · Zimmer 4.024
Tel.: 0228-73-62369
E-mail: mihatsch (add @math.uni-bonn.de)

Organization

Time: Tuesdays, 16:00 ct via Zoom

Registration: The prep meeting took place on July 16. All talks have been assigned by now, but everyone interested is welcome to attend the seminar and learn along. Please send me a brief message to obtain the Zoom link.

Content of the seminar

Seminar Program

We will learn about the classification of quadratic spaces over local and global fields (Hasse-Minkowski Theorem) and study the question of solving quadratic equations over the integers (Smith-Minkowski-Siegel Theorem). Please see the program for more information. The seminar is directed to both Bachelor and Master students. It combines nicely with the lecture Algebra II - Algebraic Number Theory. A basic knowledge of algebra is required (groups, rings, fields).

(Tentative) Schedule:
27.10. Quadratic Reciprocity
03.11. p-adic numbers
10.11. Hilbert Symbol
17.11. Quadratic Forms
24.11. Forms over Q_p
01.12. Forms over Q -- Hasse-Minkowski Theorem
08.12. Quadratic Lattices
15.12. Genus and Representations
22.12. Adelic description of the genus I
-- Christmas Break --
12.01. Adelic description of the genus II
19.01. The Smith-Minkowski-Siegel Theorem
26.01. Applications

Accreditation

The seminar is categorized as S2A3 (Bachelor) and S4A5 (Master).