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Hopf-Galois theory and applications to number theory
(PhD Course)

During November and December 2025, I taught the PhD course 'Hopf-Galois theory and applications to number theory' together with Cornelius Greither at the University of Pisa.​

In this web page materials and useful information on the course can be found.

Relevant information:

Title: Hopf-Galois theory and applications to number theory.

Instructors: Daniel Gil Muñoz and Cornelius Greither.

Format: Presential.

Duration: 30 hours (15 lectures, 2 hours long each).

Place: Dipartimento di Matemàtica, Università di Pisa.

Areas: Hopf algebras, Galois theory, group theory, number theory.

MSC2010: 11R32, 12F10, 16T05.​

Relevant links:

PhD courses at Università di Pisa.

Summary, syllabus and references.

Notes:

Chapter 1.

Chapter 2.

Chapter 3.

Book of notes.

Lists of exercises:

List 1: Galois theory.

List 2: Hopf algebras.

List 3: Hopf-Galois structures and Greither-Pareigis theory.

List 4: Applications of Greither-Pareigis theorem.

List 5: Hopf-Galois module theory.

Schedule of the lectures:

  • Lecture 1: Thursday, Nov 6, 2025, 16:00-18:00. Aula Riunioni. Lecturer: Daniel Gil Muñoz.

  • Lecture 2: Thursday, Nov 13, 2025, 16:00-18:00. Aula Riunioni. Lecturer: Daniel Gil Muñoz.

  • Lecture 3: Friday, Nov 14, 2025., 14:00-16:00 Aula Riunioni. Lecturer: Cornelius Greither.

  • Lecture 4: Tuesday, Nov 18, 2025, 16:00-18:00. Aula Riunioni. Lecturer: Cornelius Greither.

  • Lecture 5: Wednesday, Nov 19, 2025, 14:00-16:00. Aula Magna. Lecturer: Cornelius Greither.

  • Lecture 6: Thursday, Nov 20, 2025, 16:00-18:00. Aula Magna. Lecturer: Cornelius Greither.

  • Lecture 7: Friday, Nov 21, 2025, 9:00-11:00. Aula Riunioni. Lecturer: Cornelius Greither.

  • Lecture 8: Monday, Nov 24, 2025, 11:00-13:00. Aula Riunioni. Lecturer: Daniel Gil Muñoz.

  • Lecture 9: Thursday, Nov 27, 2025, 16:00-18:00. Saletta Riunioni. Lecturer: Daniel Gil Muñoz.

  • Lecture 10: Monday, Dec 1, 2025, 11:00-13:00. Aula O1 (Polo Fibonacci). Lecturer: Daniel Gil Muñoz.

  • Lecture 11: Thursday, Dec 4, 2025, 16:00-18:00. Aula O1 (Polo Fibonacci). Lecturer: Daniel Gil Muñoz.

  • Lecture 12: Thursday, Dec 11, 2025, 16:00-18:00. Aula Riunioni. Lecturer: Daniel Gil Muñoz.

  • Lecture 13: Friday, Dec 12, 2025, 11:00-13:00. Aula Riunioni. Lecturer: Daniel Gil Muñoz.

  • Lecture 14: Monday, Dec 15, 2025, 11:00-13:00. Saletta Riunioni (piano terra). Lecturer: Daniel Gil Muñoz.

  • Lecture 15: Thursday, Dec 18, 2025, 16:00-18:00. Saletta Riunioni (piano terra). Lecturer: Daniel Gil Muñoz.

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