Notes 

Some notes for Graduate topics . 

• Symmetric monoidal oo-categories and 3 functor formalism
  notes for a talk for a workshop on the 6 Functor Formalism organised by Geoffroy Horel at Université Sorbonne Paris Nord.
  → Chapter III of Scholze's notes. Definition of symmetric monoidal oo-categories, lax s.m. functor into a cartesian s.m. oo-category, 3 functor formalism (examples and explicit computations).

• dg Lie algebras and dg coalgebras
  notes for a preparatory talk I gave for the European Autumn School in Topology 2023.
  → dgLie, dgCoalg, Koszul Duality, Milnor-Moore and Cartan-Serre theorems, Quillen's dg Lie algebra associated to a simply connected space X.
  [Ref: Alexander Berglund's lecture notes on Rational Homotopy Theory]

• Homotopy-coherent algebras via Segal condition [summary and extended notes]
  notes for a talk on the homonymous article by Chu and Haugseng (see arXiv)
  Talk given for the Freudenthal topology seminar in Utrecht.
  → Sections 1 to 9 of the article: algebraic patterns, Segal objects, (weak) Segal fibrations, free Segal objects, examples. 

• Exith Path functor for conically stratified spaces
  notes for a talk for a workshop on the article 'A Stratified Homotopy Hypothesis' of Rayala, Francis and Rozenblyum (see arXiv), organized by Sylvain Douteau at Université Paris Cité.
  → Section 3 of the same article: construction of the Exit Path functor + extended proofs + open questions

Some notes and exercises from my Undergraduate studies. Enjoy! :)

• • Exercises in homological and commutative algebra
    for the course  Advanced Algebra of Prof. T. Szamuely, ay 2020/21, @ Università di Pisa.

  • Exercises in Sheaf Theory
    for the course of Schemes of Prof. Angelo Vistoli, ay 2020/21 @ SNS [in italian].

  • (oo,1)-categories: motivations
    slides for the course Category Theory of Prof. Valerio Melano, ay 2020/21 @ Università di Pisa [in italian].

  • Positive-Stellensatz e Real-Nullstellensatz for real closed fields
    some handwritten notes [in italian].

  • Exercises in Differential Geometry and Topology (curves and surfaces)
    for the homonymous course of Prof. Enrico Le Donne, ay 2019\2020, @ Università di di Pisa [in italian].

  • Equality in Homotopy Type Theory
    on homotopy equivalence, judgmental equality, propositional equality [in italian].

  • The Riemann Sphere
    some notes from the course of Geometry and Topology of Prof. Broglia and Prof. Gandini, ay 2018/19 @ Università di Pisa [in italian].

  • An Excercise on inference rules.

Have a look at my Bachelor Thesis on Homotopy Type Theory .

The construction of Real Numbers in Homotopy Type Theory.

Advisor: Professor Marcello Mamino.