From fee7a2800565a21a39e11cd1beec358111a1a01f Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Sun, 20 Feb 2022 18:50:47 +0100 Subject: Initial commit --- src/research/notes-bilbao.pdf | Bin 0 -> 236060 bytes src/research/notes-division-modules.pdf | Bin 0 -> 275589 bytes src/research/notes-etale.pdf | Bin 0 -> 241921 bytes src/research/notes-injectivity.pdf | Bin 0 -> 265097 bytes src/research/notes-katz.pdf | Bin 0 -> 212085 bytes src/research/notes-kummerec.pdf | Bin 0 -> 184812 bytes src/research/research.md | 109 ++++++++++++++++++++++++++++++ src/research/slides-alggroupsfieldext.pdf | Bin 0 -> 286305 bytes src/research/slides-ecm.pdf | Bin 0 -> 402156 bytes src/research/slides-fieldextec.pdf | Bin 0 -> 6229399 bytes src/research/slides-groupcohomec.pdf | Bin 0 -> 214734 bytes src/research/slides-kummec-barcelona.pdf | Bin 0 -> 296870 bytes src/research/slides-kummec-diamant.pdf | Bin 0 -> 276579 bytes src/research/slides-kummerdegrees.pdf | Bin 0 -> 297819 bytes src/research/slides-local-global.pdf | Bin 0 -> 611694 bytes src/research/slides-tronto-bristol.pdf | Bin 0 -> 244161 bytes 16 files changed, 109 insertions(+) create mode 100644 src/research/notes-bilbao.pdf create mode 100644 src/research/notes-division-modules.pdf create mode 100644 src/research/notes-etale.pdf create mode 100644 src/research/notes-injectivity.pdf create mode 100644 src/research/notes-katz.pdf create mode 100644 src/research/notes-kummerec.pdf create mode 100644 src/research/research.md create mode 100644 src/research/slides-alggroupsfieldext.pdf create mode 100644 src/research/slides-ecm.pdf create mode 100644 src/research/slides-fieldextec.pdf create mode 100644 src/research/slides-groupcohomec.pdf create mode 100644 src/research/slides-kummec-barcelona.pdf create mode 100644 src/research/slides-kummec-diamant.pdf create mode 100644 src/research/slides-kummerdegrees.pdf create mode 100644 src/research/slides-local-global.pdf create mode 100644 src/research/slides-tronto-bristol.pdf (limited to 'src/research') diff --git a/src/research/notes-bilbao.pdf b/src/research/notes-bilbao.pdf new file mode 100644 index 0000000..5c0500c Binary files /dev/null and b/src/research/notes-bilbao.pdf differ diff --git a/src/research/notes-division-modules.pdf b/src/research/notes-division-modules.pdf new file mode 100644 index 0000000..0883299 Binary files /dev/null and b/src/research/notes-division-modules.pdf differ diff --git a/src/research/notes-etale.pdf b/src/research/notes-etale.pdf new file mode 100644 index 0000000..6b31e10 Binary files /dev/null and b/src/research/notes-etale.pdf differ diff --git a/src/research/notes-injectivity.pdf b/src/research/notes-injectivity.pdf new file mode 100644 index 0000000..bb222e4 Binary files /dev/null and b/src/research/notes-injectivity.pdf differ diff --git a/src/research/notes-katz.pdf b/src/research/notes-katz.pdf new file mode 100644 index 0000000..c248b71 Binary files /dev/null and b/src/research/notes-katz.pdf differ diff --git a/src/research/notes-kummerec.pdf b/src/research/notes-kummerec.pdf new file mode 100644 index 0000000..9a91d78 Binary files /dev/null and b/src/research/notes-kummerec.pdf differ diff --git a/src/research/research.md b/src/research/research.md new file mode 100644 index 0000000..d9dc6e4 --- /dev/null +++ b/src/research/research.md @@ -0,0 +1,109 @@ +# Research + +After obtaining a bachelor degree in Trento in 2016 I have completed the +[ALGANT](https://algant.eu) Master Program (Milano and Leiden), with special +focus on number theory and algebraic geometry. I am now working on my PhD +under the supervision of [Antonella Perucca](http://antonellaperucca.net) and +[Peter Bruin](https://www.math.leidenuniv.nl/~pbruin). + +## Publications and preprints + +* Tronto, Sebastiano. + *Division in modules and Kummer theory.* + [arXiv preprint](https://arxiv.org/abs/2111.14363). + +* Lombardo, Davide; Tronto, Sebastiano. + *Some uniform bounds for elliptic curves over Q.* + [arXiv preprint](https://arxiv.org/abs/2106.09950v1). + +* Lombardo, Davide; Tronto, Sebastiano. + *Effective Kummer theory for elliptic curves.* + International Mathematics Research Notices (2021). + +* Hörmann, Fritz; Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. + *Explicit Kummer theory for quadratic fields.* + JP Journal of Algebra, Number Theory and Applications (2021). + +* Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. + *The degree of Kummer extensions of number fields.* + International Journal of Number Theory (2021). + +* Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. + *Kummer Theory for number fields via entanglement groups.* + Manuscripta Mathematica (2021). + +* Tronto, Sebastiano. + *Radical entanglement for elliptic curves.* + [arXiv preprint](https://arxiv.org/abs/2009.08298). + +* Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. + *Kummer theory for number fields.* + Proceedings of the Roman Number Theory Association (2020). + +* Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. + *Addendum to: Reductions of Algebraic integers.* + Journal of Number Theory (2020). + +* Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. + *Explicit Kummer theory for the rational numbers.* + International Journal of Number Theory (2020). + +## Talks + +* *A category of division modules*. + University of Luxembourg Number Theory seminar, November 2021. + [Notes: [pdf](notes-division-modules.pdf)] + +* *Introduction to étale cohomology*. + University of Luxembourg seminar series on perverse sheaves, October 2021. + [Notes: [pdf](notes-etale.pdf)] + +* *A generalization of injective modules*. + University of Luxembourg Number Theory seminar, October 2021. + [Notes: [pdf](notes-injectivity.pdf)] + +* *Integer factorization and elliptic curves*. + University of Leiden Bachelor seminar (guest talk), April 2021. + [Slides: [pdf](slides-ecm.pdf)] + +* *Group cohomology and elliptic curves*. + Invited talk at Number Theory Online conference, February 2021. + [Slides: [pdf](slides-groupcohomec.pdf); + Video: [link](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](slides-tronto-bristol.pdf)] + +* *Algebraic groups and field extensions*. + University of Luxembourg PhD seminar (online), April 2020. + [Slides: [pdf](slides-alggroupsfieldext.pdf)] + +* *Field extensions and elliptic curves*. + University of Luxembourg PhD Day, October 2019. + [Slides: [pdf](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](notes-kummerec.pdf); + Slides DIAMANT: [pdf](slides-kummec-diamant.pdf); + Slides Barcelona: [pdf](slides-kummec-barcelona.pdf);]. + +* *Divisibility of points in algebraic groups*. + Invited talk at the University of the Basque Country, May 2019. + [Notes: [pdf](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](slides-kummerdegrees.pdf)] + +* *The local-global principle*. + University of Luxembourg interdisciplinary seminar, March 2019. + [Slides: [pdf](slides-local-global.pdf)] + +* *Local-global principle for torsion*. + University of Luxembourg Number Theory seminar, November 2018. + [Notes: [pdf](notes-katz.pdf)] diff --git a/src/research/slides-alggroupsfieldext.pdf b/src/research/slides-alggroupsfieldext.pdf new file mode 100644 index 0000000..2b48adb Binary files /dev/null and b/src/research/slides-alggroupsfieldext.pdf differ diff --git a/src/research/slides-ecm.pdf b/src/research/slides-ecm.pdf new file mode 100644 index 0000000..9305984 Binary files /dev/null and b/src/research/slides-ecm.pdf differ diff --git a/src/research/slides-fieldextec.pdf b/src/research/slides-fieldextec.pdf new file mode 100644 index 0000000..6b54ff7 Binary files /dev/null and b/src/research/slides-fieldextec.pdf differ diff --git a/src/research/slides-groupcohomec.pdf b/src/research/slides-groupcohomec.pdf new file mode 100644 index 0000000..72a2a3c Binary files /dev/null and b/src/research/slides-groupcohomec.pdf differ diff --git a/src/research/slides-kummec-barcelona.pdf b/src/research/slides-kummec-barcelona.pdf new file mode 100644 index 0000000..7af439d Binary files /dev/null and b/src/research/slides-kummec-barcelona.pdf differ diff --git a/src/research/slides-kummec-diamant.pdf b/src/research/slides-kummec-diamant.pdf new file mode 100644 index 0000000..d66f002 Binary files /dev/null and b/src/research/slides-kummec-diamant.pdf differ diff --git a/src/research/slides-kummerdegrees.pdf b/src/research/slides-kummerdegrees.pdf new file mode 100644 index 0000000..2b13012 Binary files /dev/null and b/src/research/slides-kummerdegrees.pdf differ diff --git a/src/research/slides-local-global.pdf b/src/research/slides-local-global.pdf new file mode 100644 index 0000000..32a84fd Binary files /dev/null and b/src/research/slides-local-global.pdf differ diff --git a/src/research/slides-tronto-bristol.pdf b/src/research/slides-tronto-bristol.pdf new file mode 100644 index 0000000..4ece0b7 Binary files /dev/null and b/src/research/slides-tronto-bristol.pdf differ -- cgit v1.3