1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
|
# 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 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: [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, 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)]
|
