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].
Wed, 8th Feb | Thu, 9th Feb | Fri, 10th Feb | |
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09:30–10:30 | registration | Angella | Hasler |
10:30–11:00 | opening/coffee break | coffee break | coffee break |
11:00–12:00 | Gourgoulhon | Ferrario | Monniaux |
12:00–13:00 | Maggesi | Urban | Sacerdoti Coen |
13:00–15:00 | lunch | lunch | lunch & panel discussion |
15:00–16:00 | Zaffanella | Théry | |
16:00–17:00 | Pistone | Rodolà | |
17:00–17:30 | coffee break | coffee break | |
17:30–18:30 | Ahrens | Bergomi | |
18:30–19:30 | Speroni di Fenizio | ||
19:30– | dinner | social dinner |
Introduction to homotopy type theory (Slides)
SageMath experiments in Differential and Complex Geometry (Slides)
Word embedding: Deep Learning and Computational Topology for the evaluation of context-based semantic change
Symmetries, computers, and periodic orbits for the n-body problem (Slides)
Differential Geometry with SageMath (Slides) (Slides on running SageMath)
Overview of Computer Algebra Software for Tensor Calculus
A formalization of metric spaces in HOL (Slides) (Page on the speaker's web site)
A survey of Satisfiability Modulo Theory (Slides)
Information Geometry: background and applications in Machine Learning (Slides)
Geometric Deep Learning (Slides)
Formalizing a Result in Formal Topology in Type Theory
An introduction to Artificial Chemistries: Algebra applied to Informatics applied to Biology (Slides)
Proof Assistant and Planar Geometry (Slides)
Learning-assisted Theorem Proving and Formalization (Slides)
Polyhedra to reason about software (Slides)
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Pescara has a small airport, Abruzzo Airport, very close to downtown. If traveling directly to Abruzzo Airport is not an option (very likely!), consider going through Rome Fiumicino Airport From there, there are many bus connections (~3h 20m travel time), with either Prontobus or Di Carlo Bus.
Another option is landing in Rome Ciampino Airport: from there you can find bus connections to Pescara with Prontobus (~2h 30m). If you are in Rome but not at the airport, in addition to Prontobus and Di Carlo Bus, you may consider Flixbus and Arpa-Di Febo-Capuani-Di Fonzo buses.
Technically you could reach Pescara by train, with trains departing from Rome Tiburtina station. However, trains on the line Rome–Pescara are quite slow. On the bright side, the trip by train is interesting since trains pass trough many small rural villages in the innermost part of Italy. If you have time to spare (and no work to do... probably no Internet connection there) it could be an alternative.
If you are in Italy everywhere else, you can reach Pescara by bus with Flixbus or by train.
This is a list of hotels in downtown Pescara or near the place of the workshop.
Gianluca Amato
Università degli Studi “G. d'Annunzio”, Italy
Giovanni Bazzoni
Philipps-Universität Marburg, Germany
Marco Maggesi
Università degli Studi di Firenze, Italy
Francesca Scozzari
Università degli Studi “G. d'Annunzio”, Italy
Maurizio Parton
Università degli Studi “G. d'Annunzio”, Italy