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+# 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)]