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# Talks
## Cubing
* *Cubo di Rubik e Speedcubing (ITA)*.
Invited talk at Università di Cagliari, January 2020.
[Slides: [pdf, 2.0Mb](cubo-cagliari.pdf)]
* *The Rubik's cube group structure in 2 minutes*.
Speed talk at the AAN Symposium, May 2019.
[Slides: [pdf, 1.2Mb](cube-2min-slides.pdf)]
## Math
* *Elliptic Curves and the ECM algorithm*.
ALTEN Scientific Software Evening, February 2025.
[Slides: [html, 2.4Mb](./ecm)]
* *Kummer theory for elliptic curves*.
Short talk for Tarrach Prize 2023, March 2023.
[Slides: [pdf, 288Kb](kummer-tarrach.pdf)]
* *Kummer theory for commutative algebraic groups*.
Seminar at the university of Leiden, September 2022.
[Slides: [pdf, 1.2Mb](slides-kummer-final.pdf)]
* *My journey in Kummer theory*.
Leiden-Luxembourg Number Theory PhD Days 2022, July 5-6.
[Slides: [pdf, 521Kb](slides-journey-kummer.pdf)]
* *A tour of group theory with our companion cube*.
University of Luxembourg PhD seminar, May 2022.
[Slides: [pdf, 1.1Mb](group-cube.pdf)]
* *Kummer theory via (J,T)-extensions*.
University of Leiden algebra seminar, May 2022;
similar to *A category of division modules*, see below.
* *Kummer theory for algebraic groups*.
Nederlands Matematisch Congres, April 2022;
repeated at the DIAMANT symposium, April 2022.
[Notes (NMC): [pdf, 215Kb](slides-kummer-kwg.pdf);
Script (NMC): [txt, 9Kb](script-kummer-kwg.txt);
Notes (DIAMANT, longer version): [pdf, 223Kb](slides-kummer-diamant.pdf)]
* *Division in modules*.
University of Leiden algebra seminar, April 2022;
similar to *A generalization of injective modules* and
*Division in modules and Kummer theory*, see below.
[Notes: [pdf, 245Kb](division-leiden.pdf)]
* *Division in modules and Kummer theory*.
Invited talk at the University of Groningen, February 2022.
[Slides: [pdf, 249Kb](division-groningen.pdf)]
* *A category of division modules*.
University of Luxembourg Number Theory seminar, November 2021.
[Notes: [pdf, 270Kb](notes-division-modules.pdf)]
* *Introduction to étale cohomology*.
University of Luxembourg seminar series on perverse sheaves, October 2021.
[Notes: [pdf, 237Kb](notes-etale.pdf)]
* *A generalization of injective modules*.
University of Luxembourg Number Theory seminar, October 2021.
[Notes: [pdf, 259Kb](notes-injectivity.pdf)]
* *Integer factorization and elliptic curves*.
University of Leiden Bachelor seminar (guest talk), April 2021.
[Slides: [pdf, 393Kb](slides-ecm.pdf)]
* *Group cohomology and elliptic curves*.
Invited talk at Number Theory Online conference, February 2021.
[Slides: [pdf, 210Kb](slides-groupcohomec.pdf);
[Video](https://vimeo.com/526814236/1a640285c0?embedded=true&source=video_title&owner=47245911)]
* *Kummer theory for algebraic groups*.
Invited talk at the University of Bristol (online), October 2020.
[Slides: [pdf, 239Kb](slides-tronto-bristol.pdf)]
* *Algebraic groups and field extensions*.
University of Luxembourg PhD seminar (online), April 2020.
[Slides: [pdf, 280Kb](slides-alggroupsfieldext.pdf)]
* *Field extensions and elliptic curves*.
University of Luxembourg PhD Day, October 2019.
[Slides: [pdf, 6.0Mb](slides-fieldextec.pdf)]
* *Kummer theory for elliptic curves*.
University of Leiden algebra seminar, September 2019;
repeated with slides at the DIAMANT symposium, November 2019 and
at Seminari de Teoria de Nombres de Barcelona, February 2020.
[Notes: [pdf, 181Kb](notes-kummerec.pdf);
Slides DIAMANT: [pdf, 271Kb](slides-kummec-diamant.pdf);
Slides Barcelona: [pdf, 290Kb](slides-kummec-barcelona.pdf)].
* *Divisibility of points in algebraic groups*.
Invited talk at the University of the Basque Country, May 2019.
[Notes: [pdf, 231Kb](notes-bilbao.pdf)]
* *Kummer theory for number fields*.
Fifth symposium of the Roman Number Theory association, April 2019;
repeated at the Algant Alumni symposium in Benasque, May 2019.
[Slides: [pdf, 291Kb](slides-kummerdegrees.pdf)]
* *The local-global principle*.
University of Luxembourg interdisciplinary seminar, March 2019.
[Slides: [pdf, 598Kb](slides-local-global.pdf)]
* *Local-global principle for torsion*.
University of Luxembourg Number Theory seminar, November 2018.
[Notes: [pdf, 208Kb](notes-katz.pdf)]
## Software
* *L'importanza del software libero nella ricerca (ITA)*.
Linux day in Feltre, October 2019.
[Slides: [pdf, 804Kb](linuxday2019.pdf);
[Video](https://www.youtube.com/watch?v=FB0YIYNp3rw)]
* *Linux from scratch (ITA)*
Linux day in Sedico, October 2012.
[Video](https://www.youtube.com/watch?v=h7xW7iq-ApA).
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