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| author | Sebastiano Tronto <sebastiano@tronto.net> | 2023-05-06 17:43:11 +0200 |
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| committer | Sebastiano Tronto <sebastiano@tronto.net> | 2023-05-06 17:43:11 +0200 |
| commit | a5d66cb6da3f6ab3b79898769b4d118c8b9e498b (patch) | |
| tree | 9444326d20a56380bd44a081b3295fcfd891a3cf /src/research/research.md | |
| parent | 11f155d5a60715508a3fe2069f723f354c65bc52 (diff) | |
| download | sebastiano.tronto.net-a5d66cb6da3f6ab3b79898769b4d118c8b9e498b.tar.gz sebastiano.tronto.net-a5d66cb6da3f6ab3b79898769b4d118c8b9e498b.zip | |
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diff --git a/src/research/research.md b/src/research/research.md index 20cd1fe..ca5b4a0 100644 --- a/src/research/research.md +++ b/src/research/research.md | |||
| @@ -5,10 +5,11 @@ After obtaining a bachelor degree in Trento in 2016 I have completed the | |||
| 5 | special focus on number theory and algebraic geometry. I then moved on to | 5 | special focus on number theory and algebraic geometry. I then moved on to |
| 6 | obtain a joint PhD at the universities of Luxembourg and Leiden, under | 6 | obtain a joint PhD at the universities of Luxembourg and Leiden, under |
| 7 | the supervision of [Antonella Perucca](http://antonellaperucca.net) and | 7 | the supervision of [Antonella Perucca](http://antonellaperucca.net) and |
| 8 | [Peter Bruin](https://www.math.leidenuniv.nl/~pbruin). I have collected | 8 | [Peter Bruin](https://www.math.leidenuniv.nl/~pbruin). |
| 9 | in this page the list of papers I puplished during my PhD, as well as | 9 | |
| 10 | slides or notes for all the talks I have given and my theses (Bachelor, | 10 | I have collected in this page the list of papers I puplished during my PhD, |
| 11 | Master, PhD). | 11 | as well as theses (Bachelor, Master, PhD). See [my talks page](../talks) |
| 12 | for a list of slides and notes of my talks. | ||
| 12 | 13 | ||
| 13 | ## Theses | 14 | ## Theses |
| 14 | 15 | ||
| @@ -69,100 +70,3 @@ Master, PhD). | |||
| 69 | * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. | 70 | * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. |
| 70 | *Explicit Kummer theory for the rational numbers.* | 71 | *Explicit Kummer theory for the rational numbers.* |
| 71 | International Journal of Number Theory (2020). | 72 | International Journal of Number Theory (2020). |
| 72 | |||
| 73 | ## Talks | ||
| 74 | |||
| 75 | * *Kummer theory for elliptic curves*. | ||
| 76 | Short talk for Tarrach Prize 2023, March 2023. | ||
| 77 | [Slides: [pdf, 288Kb](kummer-tarrach.pdf)] | ||
| 78 | |||
| 79 | * *Kummer theory for commutative algebraic groups*. | ||
| 80 | Seminar at the university of Leiden, September 2022. | ||
| 81 | [Slides: [pdf, 1.2Mb](slides-kummer-final.pdf)] | ||
| 82 | |||
| 83 | * *My journey in Kummer theory*. | ||
| 84 | Leiden-Luxembourg Number Theory PhD Days 2022, July 5-6. | ||
| 85 | [Slides: [pdf, 521Kb](slides-journey-kummer.pdf)] | ||
| 86 | |||
| 87 | * *A tour of group theory with our companion cube*. | ||
| 88 | University of Luxembourg PhD seminar, May 2022. | ||
| 89 | [Slides: [pdf, 1.1Mb](group-cube.pdf)] | ||
| 90 | |||
| 91 | * *Kummer theory via (J,T)-extensions*. | ||
| 92 | University of Leiden algebra seminar, May 2022; | ||
| 93 | similar to *A category of division modules*, see below. | ||
| 94 | |||
| 95 | * *Kummer theory for algebraic groups*. | ||
| 96 | Nederlands Matematisch Congres, April 2022; | ||
| 97 | repeated at the DIAMANT symposium, April 2022. | ||
| 98 | [Notes (NMC): [pdf, 215Kb](slides-kummer-kwg.pdf); | ||
| 99 | Script (NMC): [txt, 9Kb](script-kummer-kwg.txt); | ||
| 100 | Notes (DIAMANT, longer version): [pdf, 223Kb](slides-kummer-diamant.pdf)] | ||
| 101 | |||
| 102 | * *Division in modules*. | ||
| 103 | University of Leiden algebra seminar, April 2022; | ||
| 104 | similar to *A generalization of injective modules* and | ||
| 105 | *Division in modules and Kummer theory*, see below. | ||
| 106 | [Notes: [pdf, 245Kb](division-leiden.pdf)] | ||
| 107 | |||
| 108 | * *Division in modules and Kummer theory*. | ||
| 109 | Invited talk at the University of Groningen, February 2022. | ||
| 110 | [Slides: [pdf, 249Kb](division-groningen.pdf)] | ||
| 111 | |||
| 112 | * *A category of division modules*. | ||
| 113 | University of Luxembourg Number Theory seminar, November 2021. | ||
| 114 | [Notes: [pdf, 270Kb](notes-division-modules.pdf)] | ||
| 115 | |||
| 116 | * *Introduction to étale cohomology*. | ||
| 117 | University of Luxembourg seminar series on perverse sheaves, October 2021. | ||
| 118 | [Notes: [pdf, 237Kb](notes-etale.pdf)] | ||
| 119 | |||
| 120 | * *A generalization of injective modules*. | ||
| 121 | University of Luxembourg Number Theory seminar, October 2021. | ||
| 122 | [Notes: [pdf, 259Kb](notes-injectivity.pdf)] | ||
| 123 | |||
| 124 | * *Integer factorization and elliptic curves*. | ||
| 125 | University of Leiden Bachelor seminar (guest talk), April 2021. | ||
| 126 | [Slides: [pdf, 393Kb](slides-ecm.pdf)] | ||
| 127 | |||
| 128 | * *Group cohomology and elliptic curves*. | ||
| 129 | Invited talk at Number Theory Online conference, February 2021. | ||
| 130 | [Slides: [pdf, 210Kb](slides-groupcohomec.pdf); | ||
| 131 | Video: [link](https://vimeo.com/526814236/1a640285c0?embedded=true&source=video_title&owner=47245911)] | ||
| 132 | |||
| 133 | * *Kummer theory for algebraic groups*. | ||
| 134 | Invited talk at the University of Bristol (online), October 2020. | ||
| 135 | [Slides: [pdf, 239Kb](slides-tronto-bristol.pdf)] | ||
| 136 | |||
| 137 | * *Algebraic groups and field extensions*. | ||
| 138 | University of Luxembourg PhD seminar (online), April 2020. | ||
| 139 | [Slides: [pdf, 280Kb](slides-alggroupsfieldext.pdf)] | ||
| 140 | |||
| 141 | * *Field extensions and elliptic curves*. | ||
| 142 | University of Luxembourg PhD Day, October 2019. | ||
| 143 | [Slides: [pdf, 6.0Mb](slides-fieldextec.pdf)] | ||
| 144 | |||
| 145 | * *Kummer theory for elliptic curves*. | ||
| 146 | University of Leiden algebra seminar, September 2019; | ||
| 147 | repeated with slides at the DIAMANT symposium, November 2019 and | ||
| 148 | at Seminari de Teoria de Nombres de Barcelona, February 2020. | ||
| 149 | [Notes: [pdf, 181Kb](notes-kummerec.pdf); | ||
| 150 | Slides DIAMANT: [pdf, 271Kb](slides-kummec-diamant.pdf); | ||
| 151 | Slides Barcelona: [pdf, 290Kb](slides-kummec-barcelona.pdf)]. | ||
| 152 | |||
| 153 | * *Divisibility of points in algebraic groups*. | ||
| 154 | Invited talk at the University of the Basque Country, May 2019. | ||
| 155 | [Notes: [pdf, 231Kb](notes-bilbao.pdf)] | ||
| 156 | |||
| 157 | * *Kummer theory for number fields*. | ||
| 158 | Fifth symposium of the Roman Number Theory association, April 2019; | ||
| 159 | repeated at the Algant Alumni symposium in Benasque, May 2019. | ||
| 160 | [Slides: [pdf, 291Kb](slides-kummerdegrees.pdf)] | ||
| 161 | |||
| 162 | * *The local-global principle*. | ||
| 163 | University of Luxembourg interdisciplinary seminar, March 2019. | ||
| 164 | [Slides: [pdf, 598Kb](slides-local-global.pdf)] | ||
| 165 | |||
| 166 | * *Local-global principle for torsion*. | ||
| 167 | University of Luxembourg Number Theory seminar, November 2018. | ||
| 168 | [Notes: [pdf, 208Kb](notes-katz.pdf)] | ||
