# Lorenzo Stefanello

Doctor in Mathematics

## Home

Hi! My name is Lorenzo Stefanello. I recently obtained my PhD in Mathematics from Università di Pisa, with the dissertation *Hopf–Galois Structures, Skew Braces, and Their Connection*. My supervisors were Prof. Ilaria Del Corso and Dr. Paul J. Truman.

My research lies at the intersection of abstract algebra and algebraic number theory. In particular, I am interested in (the interplay between)

*Hopf–Galois structures*, which have been shown to have a great impact in Galois module theory*skew braces*, recently introduced objects of group theoretic flavour related to solutions of the Yang–Baxter equation

My email is lorenzo.stefanello@phd.unipi.it. Here you can find my CV and a list of my profiles:

## Work

- LS and Cindy (Sin Yi) Tsang,
*Classification of the types for which every Hopf–Galois correspondence is bijective*

Preprint (2024) - I. Del Corso and LS,
*On Fuchs' problem for finitely generated abelian groups: The small torsion case*

Preprint (2024) - LS and Senne Trappeniers,
*On the connection between Hopf–Galois structures and skew braces*

Bulletin of the London Mathematical Society 55 (2023), no. 4, 1726–1748 (arXiv version) - A. Caranti and LS,
*Skew braces from Rota–Baxter operators: a cohomological characterisation and some examples*

Annali di Matematica Pura ed Applicata (4) 202 (2023), no. 1, 1–13 (arXiv version) - LS and S. Trappeniers,
*On bi-skew braces and brace blocks*

Journal of Pure and Applied Algebra 227 (2023), no. 5, Paper No. 107295 (arXiv version) - A. Caranti and LS,
*Brace blocks from bilinear maps and liftings of endomorphisms*

Journal of Algebra 610 (2022), 831–851 (arXiv version) - A. Caranti and LS,
*From endomorphisms to bi-skew braces, regular subgroups, the Yang–Baxter equation, and Hopf–Galois structures*

Journal of Algebra 587 (2021), 462–487 (arXiv version)

My Erdős number is 4.

- In the report for Mini-Workshop: Skew Braces and the Yang–Baxter Equation you can find my extended abstract
*Hopf–Galois theory via skew braces*. - Here you can find the notes of the workshop Galois and Hopf Galois, written with F. Ferri.

## Talks

*Describing Hopf–Galois structures via skew braces*

Groups & Algebras in Bicocca for Young algebraists, 21 June 2023*Classifying Galois extensions with Childs's property*

Algebraic structures in the Yang-Baxter equation, 4 June 2024*Classifying Galois extensions with Childs's property*

Hopf algebras and Galois module theory, 31 May 2024*A relaxed introduction to Hopf–Galois theory*

Workshop on Algebra in l’AQuila 2023, 19 October 2023*The algebraic structure of skew braces*

Università degli Studi di Siena, 22 September 2023*Skew braces: From the Yang–Baxter equation to Hopf–Galois structures*

XXII Congresso dell'Unione Matematica Italiana, 4 September 2023*On notions of solubility in Hopf–Galois theory*

Skew braces, skew bracoids, and Hopf-Galois structures, 2 August 2023*Describing Hopf–Galois structures via skew braces*

Young Researchers Algebra Conference 2023, 28 July 2023*Skew braces and the Hopf–Galois correspondence*

Groups, Rings and the Yang-Baxter equation 2023, 22 June 2023*Skew braces and Rota–Baxter operators*

Advances in Group Theory and Applications 2023, 7 June 2023*Bi-skew braces in Hopf–Galois theory*

Hopf algebras and Galois module theory, 29 May 2023*Skew braces and the Hopf–Galois correspondence*

The Interplay Between Skew Braces and Hopf-Galois Theory, 18 April 2023*Hopf–Galois theory via skew braces*

Skew Braces and the Yang–Baxter Equation (Oberwolfach Mini-Workshop), 2 March 2023*Hopf–Galois theory and skew braces: Open problems and directions*

Keele University, 30 January 2023*Some explicit constructions of skew braces*

Categories, Rings and Modules, a conference in honor of Alberto Facchini, 28 January 2023*Hopf–Galois theory via (opposite) skew braces*

University of Exeter, 13 September 2022*Some new results on bi-skew braces*

The algebra of the Yang-Baxter equation, 14 July 2022*Skew braces that do not come from Rota–Baxter operators*

Ischia Group Theory 2022, 24 June 2022*Some new examples of Hopf–Galois structures in which the Hopf–Galois correspondence is surjective*

Hopf algebras and Galois module theory, 31 May 2022*On bi-skew braces and related topics*

QA Seminar (Vrije Universiteit Brussel), 18 May 2022*Skew braces, brace blocks, and the Yang–Baxter equation*

Inform on Algebra (Università del Salento), 31 March 2022*Hopf algebras, Galois modules, and skew braces*

Insalate di Matematica (Università degli Studi di Milano-Bicocca), 10 March 2022*Local Galois module theory and ramification: An overview*

Number Theory Seminar (Charles University), 25 January 2022*An explicit construction of brace blocks*

Braces in Bracelet Bay, 4 January 2022*Local Galois module theory: An overview*

Young Researchers in Algebraic Number Theory 2021, 19 August 2021*... the Yang–Baxter equation, and Hopf–Galois structures*

Hopf algebras and Galois module theory, 25 May 2021

## Links

#### Researchers, Papers, and Journals

- MathSciNet
- MR Lookup
- ORCiD
- Scopus
- arXiv
- ResearchGate
- zbMATH
- Semantic Scholar
- Web of Science
- The Mathematics Genealogy Project
- Journal Citation Reports
- SCImago
- SCI Journal
- Springer Journal Suggester

#### Conferences and Seminars

- Number Theory Web
- researchseminars
- MathMeetings
- Conference Service
- Ramification, Galois Module Structure and Hopf-Galois Theory
- Advances in Group Theory and Applications
- Galois and Hopf Galois

#### Useful Links

- Mathematics Subject Classification
- Overleaf
- Connected Papers
- Detexify
- quiver
- anvur
- Abilitazione Scientifica Nazionale
- Bandi MIUR
- Premi UMI

#### Didactics and Databases

- Mathematics StackExchange
- MathOverflow
- Groupprops
- nLab
- A Database For Number Fields
- A Database for Class Groups of Number Fields
- LMFDB: The L-functions and modular forms database
- Database of Ring Theory