Feb 04, 2020 to Feb 06, 2020

The conference intends to gather people with connected topics of interest that revolve around constructive algebra, logics, computer algebra, and algebraic geometry. The conference is organized by Peter Schuster (Università di Verona) and Ihsen Yengui (Université de Sfax), and is part of the John Templeton Foundation project "A New Dawn of Intuitionism: Mathematical and Philosophical Advances" led by Michael Rathjen (University of Leeds). Additional funding comes from the Dipartimento di Informatica of the University of Verona (http://www.di.univr.it/, http://www.univr.it/).

FOR REGISTRATION AND ALL PRACTICAL ARRANGEMENTS, PLEASE CONTACT Ihsen Yengui** : ihsen_yengui@yahoo.fr**

There will be the possibility to contribute to a poster session.

For more details, refer to the website of the conference: https://sites.google.com/view/algebralgorithms2020

**Organizing Commitee:**

Peter Schuster (Verona), Ihsen Yengui (Sfax).

**Moulay Barkatou** (Limoges), Matrices of scalar differential operators: divisibility and spaces of solutions

**Marco Benini** (Insubria), Induction on free structures

**Ulrich Berger** (Swansea), Algorithmic aspects of least and greatest fixed points

**Felix Cherubini** (Karlsruhe), Constructive cohomology of sheaves via higher inductive types

**Thomas Cluzeau** (Limoges), Isomorphic finitely presented modules, Constructively

**M'hammed El Kahoui** (Marrakech), The Zariski Cancellation problem and related topics

**Gregor Kemper** (Munich), Dimension and Monomial Orderings

**Henri Lombardi** (Besançon), Sheaves on Spectral Spaces, Constructively

**Stefan Neuwirth** (Besançon), Lorenzen's noncommutative divisibility theories

**Iosif Petrakis** (Munich), Bishop topological groups

**Thomas Powell** (Darmstadt), Goedel's functional interpretation in constructive algebra

**Alban Quadrat** (Paris), On computational aspects of stability and stabilizability of multidimensional systems

**Giuseppe Rosolini **(Genova), Groupoids as completing a fibration with identity types

For more details, refer to the website of the conference:

https://sites.google.com/view/algebralgorithms2020

Constructive algebra can be seen as an abstract version of computer algebra. In computer algebra, on the one hand, one attempts to construct efficient algorithms for solving concrete problems given in an algebraic formulation, where a problem is understood to be concrete if its hypotheses and conclusion have computational content. Constructive algebra, on the other hand, can be understood as a ``preprocessing'' step for computer algebra that leads to general algorithms, even if they are sometimes not efficient. In constructive algebra, one tries to give general algorithms for solving ``virtually any" theorem of abstract algebra. Therefore, a first task in constructive algebra is to define the computational content hidden in hypotheses that are formulated in a very abstract way. For example, what is a good constructive definition of a local ring (i.e., a ring with a unique maximal ideal), a valuation ring (i.e., a ring in which all elements are comparable under division), an arithmetical ring (i.e., a ring which is locally a valuation ring), a ring of Krull dimension at most n, and so on? A good constructive definition must be equivalent to the usual definition within classical mathematics; it must have computational content; and it must be fulfilled by ``usual" objects that satisfy the definition.

(**An extract from the introduction of the book "Constructive Commutative Algebra. Lecture Notes in Mathematics, no 2138, Springer 2015" by Ihsen Yengui**)

Feb 04, 2020 to Feb 06, 2020

No participants