some notes

Reading seminars

• Anosov representations: reading group at the University of Virginia, with Sara Maloni and Alec Traaseth. Our main reference were Dick Canary’s “informal lecture notes” on Anosov representations. Here are my notes:
  • From Part 2, Sections: 1, 2, 3, 4, 5.
  • From Part 3, Sections: 9, 10, 11, 12.
  • From Part 4, Sections: 17, 18, 19, 20, 21, 22.
  • From Part 5, Sections: 24, 25, 26, 27, 28.
• A hyperKähler extension of Teichmüller space: G&T reading group at the Université du Luxembourg in Fall 2018 and Spring 2019 semesters, organized by Binbin Xu and presented by Yan Mary He, Louis Merlin, Vincent Pecastaing, Andrea Seppi, Binbin Xu, and I. My main references were: Donaldson, Moment maps in differential geometry; Hodge, Ph.D. thesis; Trautwein, Ph.D. thesis. Here are my notes:
  • Part 1 - Outline and preliminaries on symplectic reduction.
  • Part 2 - Teichmüller space as symplectic quotient.
  • Part 3 - The almost-Fuchsian deformation space.
• Cannon-Thurston maps: G&T reading group at the Université du Luxembourg in Spring 2020 semester, organized by Miguel Acosta, Binbin Xu, and presented by Miguel Acosta, Diptaishik Choudhury, Wai Yeung Lam, Thi Hanh Vo, Binbin Xu, and I. My main reference was: Cannon, Thurston, Group invariant Peano curves. Here are my notes:
  • Part 0 - Preliminaries.
  • Part 1 - Outline of the proof.
  • Part 2 - Pseudo-Anosov diffeomorphisms.

Some Math in Italian

Disclaimer! The material appearing below is a quite random collection of notes from my Master studies at the Università di Pisa. These are NOT intended to be in any way complete references: bibliographies are not present or incomplete, they may very likely contain mistakes, and they have not been updated since I have taken these classes. Everyone is welcome to consult them, but at their own risk!

• Dehn filling iperbolico: notes from my exam of the course Geometria iperbolica, held by Bruno Martelli at the Università di Pisa in Fall 2015.
• Cenni sui modelli geometrici in dimensione 3: notes from my exam of the course 3-Varietà, held by Bruno Martelli at the Università di Pisa in Fall 2014.
• Il teorema di Cheng: notes from my exam of the course Geometria Riemanniana, held by Carlo Mantegazza and Lorenzo Mazzieri at the Scuola Normale Superiore in Pisa in Fall 2014-Spring 2015.
• Cenni sugli spazi dei moduli di superfici: notes from my exam of the course Geometria e Topologia delle superfici, held by Riccardo Benedetti at the Università di Pisa in Spring 2015.
• Appunti di Topologia Algebrica: notes from the course Topologia Algebrica, held by Mario Salvetti at the Università di Pisa in Spring 2015. Here you can also find some notes on Stiefel-Whitney and Chern classes from my exam.

Miscellaneous

Here you can find my Master thesis on the representation theory of the quantum Teichmüller space. To every native English speaker: my sincerest apologies for having barbarically murdered your language at the time (fortunately I got a bit better at it…).