FIRST ANNOUNCEMENT

Workshop "Geometry and Computer Science - GnCS 2017", Pescara, Italy, 
February 8-10, 2017

http://www.sci.unich.it/gncs2017

Geometry and computer science interact with each other in a very 
profitable way (see below). In this workshop, each talk will describe a 
challenge in geometry or computer science and explain how the other 
science helps addressing it.

*If your expertise area is geometry OR computer science, join this 
workshop* to explore new interactions between two sciences that are only 
at a first sight apart! A (limited) financial support is available for 
young researchers.

Speakers:

Daniele Angella (Università degli Studi di Firenze, Italy)
Davide Ferrario (Università degli Studi di Milano-Bicocca, Italy)
Éric Gourgoulhon (Observatoire de Paris, France)
Marco Maggesi (Università degli Studi di Firenze, Italy)
Luigi Malagò (Romanian Institute of Science and Technology, Romania), to 
be confirmed
David Monniaux (CNRS & Université Grenoble Alpes, France)
Claudio Sacerdoti Coen (Università di Bologna, Italy)
Laurent Théry (INRIA, France)
Enea Zaffanella (Università degli Studi di Parma, Italy)

Scientific Committee:

Gianluca Amato (Università degli Studi di Chieti-Pescara, Italy)
Giovanni Bazzoni (Philipps-Universität Marburg, Germany)
Marco Maggesi (Università degli Studi di Firenze, Italy)
Maurizio Parton (Università degli Studi di Chieti-Pescara, Italy)
Francesca Scozzari (Università degli Studi di Chieti-Pescara, Italy)

Register at

http://www.sci.unich.it/gncs2017/#registration

No registration fee is required.

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CONTEXT OF THE WORKSHOP

The workshop "Geometry and Computer Science" aims to deepen the 
connection between research in mathematics and research in computer science.

Computer science supports research in mathematics.
The simplest case is utilization of computer algebra systems like 
SageMath, Mathematica, Maple, that enables execution of huge amounts of 
symbolic computations.
A more sophisticated approach is using software tools to generate and 
explore conjectures [1]. This can be done in several ways: assisted 
theorem proving, proof certification, automatic theorem proving. 
Assisted proof means helping a mathematician to refine an existing line 
of proof [2,3]. Proof certification means providing internal confidence 
of an existing, complete proof [3] or of complex computations [4]. 
Automatic proof means exploring empirically the mathematical problem, to 
support intuition [5].
Beyond this, computational geometry has traditionally seen a massive 
utilization of algorithms to address geometrical problems [6].

On the other hand, geometry supports research in computer science.
Abstract interpretation, for instance, is a field where geometrical 
objects in the configuration space of the variables of a program are 
used to prove that the program is correct [7,8].
Recently, the seminal work of Voevodsky in the homotopy type theory and 
the univalent foundation of mathematics [9] showed a deep connection 
between homotopy theory (geometry), logic and theory of types (computer 
science).
Topics like neural networks and deep learning benefit from Riemannian 
optimization techniques and differential geometry [10].

[1]
Hales - Gonthier - Harrison - Wiedijk.
A special issue on formal proof.
Notices Amer. Math. Soc. 55(11), 2008.

[2]
Hales.
A proof of the Kepler conjecture.
Annals of Mathematics 162(3), 2005.

[3]
Ciolli - Gentili - Maggesi.
A certified proof of the cartan fixed point theorems.
Journal of Automated Reasoning 47(3), 2011.

[4]
Théry.
Certified version of Buchberger’s algorithm.
Automated Deduction - CADE-15, 1998.

[5]
Fuchs - Théry.
A Formalization of Grassmann-Cayley Algebra in COQ and Its Application 
to Theorem Proving in Projective Geometry.
Automated Deduction in Geometry: 8th International Workshop, 2011.

[6]
Boucetta - Morvan.
Differential Geometry and Topology, Discrete and Computational Geometry.
IOS press, 2005.

[7]
Rodríguez-Carbonell - Kapur.
Automatic generation of polynomial invariants of bounded degree using 
abstract interpretation.
Science of Computer Programming, 64(1), 2007.

[8]
Cousot - Halbwachs.
Automatic discovery of linear restraints among variables of a program.
http://www.di.ens.fr/~cousot/COUSOTpapers/POPL78.shtml, 1978.

[9]
Univalent Foundations of Mathematics.
Homotopy Type Theory.
https://homotopytypetheory.org/book, 2013.

[10]
Luigi Malagò.
Research Project "Riemannian Optimization Methods for Deep Learning".
http://rist.ro/en/details/news/postdoc-positions-in-machine-learning-optimization-deep-learning-and-information-geometry.html, 
2016.
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