# Blog de la Biblioteca de Matemàtiques i Informàtica

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

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.

## SIMBa: An introduction to theorem provers

El proper dimecres, 2 de juny, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Eloi Torrents
Universitat: Universitat Autònoma de Barcelona

Data: Wednesday, June 2nd, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: An introduction to theorem provers
Resum: In this talk, we will introduce proof assistants, pieces of softwarethat formally verify mathematical proofs.Lean has a very extensivedatabase with mathematical results at the undergraduate level for-mally verified, and it is even used to verify new research. This hasseveral applications, including teaching, automatically verifying publi-cations, and even automated theorem proving. At the end of this talk,we will carry out a demo of Lean to show the basics and how you canget started.

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.