## Dasgupta-Kakde proof of the Hilbert 12 problem

We plan to run a seminar on the recent proof of Dasgupta-Kakde of the 12th Hilbert problem for totally real extensions. For more information, write to Luca dall'Ava dallava@math.unipd.it or Matteo Longo matteo.longo@unipd.it

Talk I (M. Longo). Thursday March 24, 2022, 10:30-11:30, 2AB40.

Talk II (M. Longo). Thursday March 31, 2022, 10:30-11:30, 2AB40.

Talk III (M. Longo). Thursday April 7, 2022, 10:30-11:30, 2AB40.

Talk IV (M. Longo, L. dall'Ava). Thursday April 7, 2022, 10:30-11:30, 2AB40.

Talk V (L. dall'Ava). Thursday April 14, 2022, 10:30-11:30, 2AB40.

Talk VI (L. dall'Ava). Thursday April 21, 2022, 10:30-11:30, 2AB40.

Talk VII (M. Baracchini) Thursday May 5, 2022, 10:30-11:30, 2AB40

Talk VIII (R. Walchek) Thursday May 12, 2022, 10:30-11:30, 2AB40

Talk IX (F. Zerman) Thursday May 19, 2022, 10:30-11:30, 2AB40

Talk X (S. Wang) Thursday May 19, 2022, 10:30-11:30, 2AB40

Talk XI (M.-R. Pati) Thursday June 23, 2022, 10:30-11:30, 2AB40

**PD GDL 2021**

The aim of this seminar is to understand a new proof of the Mordell conjecture due to Lawrence and Venkatesh published in 2020.

Please check **here** for further information.

**p-adic representations and arithmetic D-modules - Prof. Francesco Baldassarri and Andrés Sarrazola Alzate **

The aim of the seminar is to give an introduction to the theory of representations of p-adic locally analytic groups and the theory of D-cap-modules for smooth rigid analytic spaces developed by Ardakov-Wadsley. We also aim to study localisation of admissible (locally analytic) representation in the sens of Huyghe-Patel-Schmidt-Strauch. The foundations in these subjects were done by P. Schneider, J. Teitelbaum, K. Ardakov, S. Wadsley, C. Huyghe, D. Patel, T. Schmidt, M. Strauch and S. Orlik whose articles will be our main references.

Please check **here** for further information.

**p-adic interpolation of modular forms - Giacomo Graziani **

First meeting October 9, 2020 - 14:30. Next meetings: every Friday at 14:30 https://unipd.zoom.us/j/81070830645 For the password, please contact Alessandra Bertapelle.

**Prisms and prismatic cohomology **

November 5, 2019 - room SR 701 - time: 14:00 - Nicola Mazzari November 12, 2019 - room SR 701 - time: 14:30 - Carolina Rivera November 26, 2019 - room SR 701 - time: 14:00 - Carolina Rivera December 16, 2019 - room 430 - time: 14:00 - Carolina Rivera January 15, 2020 - room 430 - time: 14:30 - Nicola Mazzari January 23, 2020 - roomv2AB45 - time: 14:30 - Nicola Mazzari

**From Berkovich to Moduli **

October 16, 2018 - room SR701 - 10:30 - Alessandra Bertapelle - A gentle introduction to Berkovich spaces I. October 23, 2018 - room SR701 - 10:30 - Alessandra Bertapelle - A gentle introduction to Berkovich spaces II. November 6, 2018 - room 1A150 - 12:30 - Alessandra Bertapelle - A gentle introduction to Berkovich spaces III. November 13, 2018 - room SR701 - 10:30 - Velibor Bojkovich - On the structure of smooth k-analytic curves. November 20, 2018 - room SR701 - 11:00 - Stefano Urbinati - Introduction to Tropical Geometry, I. November 27, 2018 - room SR701 - 11:30 - Carla Novelli - Introduction to Tropical Geometry, II. December 4, 2018 - room SR701 - 10:30 - Ernesto Mistretta - Introduction to Toric Varieties. December 11, 2018 -room SR701I - 10:30 - Stefano Urbinati - Introduction to Toric Varieties, II. December 18, 2018 - room SR701 - 11:00 - Stefano Urbinati - Compactification of Toric Varieties. January 15, 2019 - room SR701 - 10:30 - Orsola Tommasi - An introduction to moduli spaces in algebraic geometry. January 22, 2019 - room 1BC45 - 10:00 - Paolo Rossi - Moduli spaces of curves. January 29, 2019 - room 1C150 - 10:00 - Orsola Tommasi - Moduli space of tropical curves. February 5, 2019 - room 2AB40 - 10:30 - Orsola Tommasi - Tropicalization of the moduli space curves. February 20, 2019 - room 1BC50 - 14:00 - Orsola Tommasi - Berkovich skeleton of the moduli space of curves. April 15, 2019 - room SR701 - 13:30 - Daniele Turchetti - ** Universal Mumford curves over $\mathbb Z$ and moduli of tropical curves.**