Paolo Bordignon

About

I am a PhD student at Leiden University under the supervision of Jan Vonk.
My research interest lies in Algebraic Number Theory and Arithmetic Geometry in the broadest sense.
I am mainly interested in everything that revolves around elliptic curves, modular curves, modular forms and L-functions.

Talks

• \(p\)-adic Modular Forms and their geometry - ALGANT Symposium 2025 (slides)
• Group schemes à la Mazur I - Reynaud's theorem- Séminaire Mazur Leiden (notes)
• Group schemes à la Mazur II - Admissible groups - Séminaire Mazur Leiden (notes)
• Computation of Heegner Points - Number Theory Seminar Leiden

Seminars organised

• Study group on étale and crystalline cohomology (link)
  
• Séminaire Mazur (with Jan Vonk) (link)
  
• Class Field Theory study group
  

Education

• Ph.D. in Mathematics, Leiden University, 2023 -
• M2 in Mathematics, Paris-Saclay Universitè, 2022 - 2023 (ALGANT)
Master Thesis Two-variable p-adic L-functions with Prof. Pierre Charollois (IMJ-PRG)
• M.sc in Mathematics, Leiden University, 2021 - 2022 (ALGANT)
• B.Sc. in Mathematics, University of Udine, 2018 - 2021

Notes and code

Here are some notes I am working on. These are early draft versions, preliminary versions with possible errors.
Please email me if you spot any errors or mistakes!

• Hypercohomology of Modular Curves (pdf)
• Gauss-Manin connection for family of Elliptic Curves (pdf)
• Torsion points of prime order on Elliptic Curves (pdf)
• Group schemes à la Mazur (pdf)

Github (under construction)

• Computing Frobenius action on de Rham cohomology of Elliptic Curves (Sage)
  
• Computing Gauss-Manin connection for families of Hyperelliptic curves (Sage)
  
• Computing Heegner points (GP/Pari)
  
• Computing 2-adic eigenforms (GP/Pari)
  

Community service

Peer-reviewed an article for Int. Journal of Number Theory