Currently I am a Post-Doc in the *Arbeitsgruppe*
Topologie und Geometrie

at the
Johannes Gutenberg University (JGU), Mainz,
as part of the project SFB/TRR 45.

My research is about the arithmetic of del Pezzo and K3 surfaces.

I completed my PhD on July 5, 2016,
under the supervision of
Ronald van Luijk,
and Bert van Geemen,

it was part of the ALGANT program.

## Contact information:##
Office: | Institut für Mathematik, Room 04.427 | Office hours: | Monday, 14:00-16:00. | Telephone: | +49 (0)6131 39 23337 | E-mail: | dfesti | at uni-mainz dot de Address: | Staudingerweg 9, 55128, Mainz, Germany | Mailing address: | Institut für Mathematik
Johannes Gutenberg-Universität Mainz,
55099 Mainz | CV: | My curriculum vitae | |

- A practical algorithm to compute the geometric Picard lattice of K3 surfaces of degree 2, arXiv:1808.00351.
- On the arithmetic of a family of degree-two K3 surfaces, with Florian Bouyer, Edgar Costa, Chris Nicholls, Mckenzie West,
*Mathematical proceedings of the Cambridge Philosophical Society*, 1-20. Accompanying MAGMA code. - Unirationality of del Pezzo surfaces of degree 2 over finite fields , Bulletin of London mathematical society, volume 48, no.1 (2016), 135-140, with Ronald van Luijk.
- Unirationality of del Pezzo surfaces of degree 2 over finite fields (extended version), arXiv:1408.0269, with Ronald van Luijk.
- The Cayley-Oguiso automorphism of positive entropy on a K3 surface, Journal of Modern Dynamics, volume 7, no. 1 (2013), 75-97, with Alice Garbagnati, Bert van Geemen and Ronald van Luijk.

- Summer school International summer school on arithmetic geometry, September 2018, Università degli study di Salerno, with Ariyan Javanpeykar and Davide Veniani.
- Autumn school Topics in arithmetic and algebraic geometry, October 2017, JGU Mainz, with Ariyan Javanpeykar and Davide Veniani.
- Seminar on K3 surfaces, Fall 2014, Universiteit Leiden, with Erik Visse.
- Seminar on modular forms, Spring 2013, Universiteit Leiden, with Pinar Kilicer.

- An algorithm to compute the Picard lattice of a genus two K3 surface, Joint meeting, Wrocław. (2018).
- Computing the Picard lattice of a genus two K3 surface, Lectures on computational aspects of algebraic geometry, University of Zagreb. (2018).
- The Picard lattice of another family of double covers of the projective plane, Seminario di Natale 2017, Università Statale di Milano (2017).
- The Derived Global Torelli theorem, Seminar on derived categories in algebraic geometry, JGU Mainz (2017).
- Potential density of rational points on K3 surfaces, ALGANT meeting, Regensburg University (2015). Slides
- An algorithm to compute isomorphism groups of K3 surfaces, Seminar on K3 surfaces, Universiteit Leiden (2015).
- Rational points on K3 surfaces, Università di Salerno (2014).
- Computing the Néron-Severi group: a concrete example, Seminar on K3 surfaces, Universiteit Leiden (2014). Notes.
- Néron-Severi group of a K3 surface, Seminar on K3 surfaces, Universiteit Leiden (2014). Notes.
- Unirationality of del Pezzo surfaces of degree 2 over finite fields, ALGANT meeting, Università degli studi di Milano (2014). Slides
- Unirationality of del Pezzo surfaces of degree 2, Diamant symposium, Conference Center De Werelt, Lunteren (2013).
- Complex Multiplication for Elliptic Curves, seminar on Complex Multiplication, Universiteit Leiden (2013).
- Conductor of an elliptic curve and modularity, seminar on Modular Forms, Universiteit Leiden (2013).
- Modular curves and moduli spaces, seminar on Modular Forms, Universiteit Leiden (2013).
- Elliptic modular curves as Riemann surfaces, seminar on Modular Forms, Universiteit Leiden (2013).
- Arakelov intersection theory for Dedekind domains, seminar on Arithemitc Intersection theory, Vrij Universiteit (2012).
- Density of rational points on a family of diagonal quartic surfaces, master thesis defense, Universiteit Leiden (2012). Slides

- Topology (Fall 2018), JGU Mainz course by Cynthia Hog-Angeloni, teaching assistant.
- Elliptic curves (August 2018), Nesin Math Village course, lecturer. Notes.
- Sheaf cohomology (Spring 2018), JGU Mainz course, with Davide Cesare Veniani, lecturer.
- Elliptic curves in cryptography (April 2018), AIMS course, Senegal, with Matija Kazalicki, lecturer.
- Schemes and divisors (Fall 2017), JGU Mainz course, with Davide Cesare Veniani, lecturer.
- Elliptic curves (August 2017), Nesin Math Village course, lecturer. Notes.
- Algebraic geometry (Spring 2017), JGU Mainz reading course, with Davide Cesare Veniani, lecturer.
- Algebraic geometry (Fall 2016), JGU Mainz reading course, with Davide Cesare Veniani, lecturer.
- Number theory (Fall 2016), JGU Mainz course, by Stefan Müller-Stach , teaching assistant.
- Elliptic curves in cryptography (November 2016), AIMS course, Senegal, with Filip Najman, co-lecturer.
- Elliptic curves (August 2014), Nesin Math Village course, lecturer.
- Rational points on varieties (Fall 2013), Wonder course by Sander Dahmen and Ronald van Luijk, teaching assistant.
- Algebra 1 (Spring 2013), Universiteit Leiden course, by Ronald van Luijk, teaching assistant.
- Elliptic curves (Spring 2012), Universiteit Leiden course by David Holmes and Rachel Newton, teaching assistant.

- My PhD thesis (2016): Topics in the arithmetic of del Pezzo and K3 surfaces.
Supervisor: Ronald van Luijk, Bert van Geemen.

The MAGMA code accompanying the thesis.

Errata. - Notes on Shimada's paper "An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces".
- Notes on Drinfeld modules.
- My master thesis (2012): Density of rational points on a family of diagonal quartic surfaces. Supervisor: Ronald van Luijk.
- My bachelor thesis (in Italian, 2010): Decomposizione di interi in somme di potenze. Supervisor: Patrizia Longobardi.

Since 2013, I am carrying a didactic experimentation for high schools, at
Liceo scientifico 'Giovanni da Procida', Salerno.

Below you can find the experimentation proposals and the final reports since 2015
(all in Italian).

Here you can find a newspaper article about it (in Italian).

Any question or comment about the project is highly appreciated.