The theory of quadratic forms and central simple algebras over general fields is based to a large extent on elementary arguments. Nevertheless, many great theorems in this area are full of mysteries. Often they tell us the existence of some representation for certain objects, but the proof does not provide us with such a representation.
Constructive mathematics is an active branch of research concerned with the systematic search for computational proofs. Here the Law of the Excluded Middle and the Axiom of Choice have to be avoided. From a computational proof, one can usually extract extra information. For example, if the statement is about some way to represent a certain object, then a constructive proof will show us how to find such a representation and give us a bound on the number of parameters involved in the description.
In the summer school, general background and specific techniques from constructive algebra will be explained and linked to concrete open quantitative problems in quadratic form theory.
The programme will include a glimpse into topos theory and its role in mathematical logic. It will be tailored to young researchers in quadratic form theory and it will open perspectives for future research.
Date: 5 - 9 September 2022
Location: Stadscampus, University of Antwerp, Belgium
Speakers:
- Sylvy Anscombe (Université de Paris)
- Karim Johannes Becher (UAntwerpen)
- Ingo Blechschmidt (Augsburg University, Germany)
- Jean-Pierre Tignol (UC Louvain, Belgium)