ALGAR Summer School

In 2022, the ALGAR summer school aims to present ideas and techniques from constructive mathematics in relation to open problems in quadratic form theory. 

Date: 5 - 9 September 2022

Location: Stadscampus, University of Antwerp, Belgium


Content description

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.


The summer school will start on Monday the 5th of September in the morning and will end on Friday the 9th of September in the afternoon.

A schedule will be announced soon.

Target group

Master students and PhD students in pure mathematics. Also more experienced mathematicians are welcome to participate.

A hybrid summer school

We try to organise the summer school under normal circumstances. Participants who want to attend the summer school but are not able to due to travel restrictions or any uncertainties will be able to follow most of the programme online and interact during the talks.

Study credits (ECTS)

3 ECTS credits are awarded upon succesful completion of the programme. All certificates of completion are issued as a micro-credential. 

Social programme

Participants will be able to get in touch with peers attending other summer schools at the Antwerp Summer University. A visit to the beautiful city hall, a networking reception, a guided city walk, a quiz night, a football game and a day-trip to another Belgian city such as Bruges or Brussels are only some examples of these activities.

All activities of the social programme are offered free of charge, in some cases participants will be asked for a deposit which will be reimbursed upon participation to the activity.