**8 feb 2017 - 10 feb 2017**

Pescara, Italy

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)

Mattia Bergomi (Collective behavior lab, Champalimaud Research, Portugal)

Davide Ferrario (Università degli Studi di Milano-Bicocca, Italy)

Éric Gourgoulhon (Observatoire de Paris, France)

Maximilian Hasler (Université des Antilles et de la Guyane)

Luigi Malagò (Romanian Institute of Science and Technology, Romania), to be confirmed

David Monniaux (CNRS & Université Grenoble Alpes, France)

Emanuele Rodolà (USI Lugano, Switzerland)

Claudio Sacerdoti Coen (Università di Bologna, Italy)

Pietro Speroni (Bio System Analysis Group, FSU Jena, Germany)

Laurent Théry (INRIA, France)

Josef Urban (Czech Institute of Informatics, Robotics and Cybernetics, Czech Republic)

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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**Organizers:**
Gianluca Amato,
Giovanni Bazzoni,
Marco Maggesi,
Maurizio Parton,
Francesca Scozzari.

**Seminars:**
** 9 Feb 2017**

09:30 -
D. Angella:
SageMath experiments in Differential and Complex Geometry

**Speakers:**
Daniele Angella,
Mattia Bergomi,
Davide Ferrario,
Éric Gourgoulhon,
Maximilian Hasler,
Luigi Malagò,
David Monniaux,
Emanuele Rodolà,
Claudio Sacerdoti Coen,
Pietro Speroni,
Laurent Théry,
Josef Urban,
Enea Zaffanella.