SIMBa: On the possible ranks of universal quadratic forms over totally realnumber fields

30/09/2021 by blocmat Deixa un comentari

El proper dimecres, 6 d’octubre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Daniel Gil Muñoz
Universitat: Charles University in Prague

Data: Wednesday, October 6th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: On the possible ranks of universal quadratic forms over totally realnumber fields
Resum: A quadratic form $Q\left(X_{1}, \ldots, X_{n}\right)$ over the integer numbers is said to be universal if it represents all positive integers, that is, for every $a \in \mathbb{Z}_{>0}$ there is a vector $\left(\alpha_{1}, \ldots, \alpha_{n}\right) \in \mathbb{Z}^{n}$ such that $Q\left(\alpha_{1}, \ldots, \alpha_{n}\right)=a$ . The topic of universal quadratic forms is quite classical in arithmetic; for instance, Langrange’s 1770 four square theorem asserts that the sum of four squares is a universal quadratic form over $\mathbb{Z}$ . In this talk we consider the suitable generalization of universality for quadratic forms over the number ring $\mathcal{O}_{K}$ of a totally real number field $K$ and view some recent results on the possible ranks (number of variables $X_{i}$ ) of universal quadratic forms over different families of totally real number fields.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.