Deformation Theory

Place: online

Please contact us for the link.

Goal: It has been 30 years since Wiles's proof of Fermat's last theorem and now we are happy to celebrate it. This is a study group with the aim of introducing deformation theory in algebraic geometry and number theory. We will cover the deformation of Galois representations and the Serre-Tate theory of Abelian varieties.

If you have any questions or concerns, do not hesitate to reach out to us.

You can find the tentative program here. Let us know if you would be interested in giving a talk.

For a gentle introduction to the proof of Wiles and what's going on, watch the beautiful video 30 years of modularity: number theory since the proof of Fermat's Last Theorem by Frank Calegari.

Youtube playlist for the conference on Fermat's last theorem 1995.

A good blog for Serre-Tate's theory by Alex Youcis.

Tentative Schedule

Talk 1: Galois Representations - Francesco Zerman (07/01/2023)

Talk 2: Finite Flat Group Schemes - Khai Hoan Nguyen Dang (14/01/2023)

Tet Holiday

Talk 3: Deformation of Representations - Huy Dang (04/02/2023)

Talk 3': Complements to talk 3- Khai Hoan Nguyen Dang (11/02/2023) (12:00)

Talk 4: p-divisible Groups - Khanh Hung Nguyen (11/02/2023) (13:00)

Talk 5: Cohomological Interpretation- Arshay Sheth (18/02/2023)

Talk 6: Deformation of schemes - Tuan Thuong Dang (25/02/2023)

From now on, the seminar will take place at 2 pm (CET)

Talk 7: Universal Deformation Ring: Existence - Quang Khai Nguyen (04/03/2023)

Talk 8: Fppf Sheaves - Suraj Dash (11/03/2023)

Deformation of Galois Covering - Huy Dang (hero of us)

Breaktime

Talk 9: Universal Deformation Ring: Properties -Quang Khai Nguyen (25/03/2023)

Talk 10: Drinfeld’s Rigidity Lemma - Khai Hoan Nguyen Dang (01/04/2023)

Talk 11: Modularity and Fermat’s Last Theorem - Luca Mastella (08/04/2023)

Talk 12: Serre-Tate Deformation Theorem - Tuan Thuong Dang (15/04/2023)

Possible talks on Mazur's dimension conjecture proven by Gebhard Böckle, Ashwin Iyengar, Vytautas Paškūnas (TBD)

Talk 13: Geometric Invariant Theory - Suraj Dash

Talk 14: On local Galois deformation rings