Past working seminars

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Work group on Fargues-Fontaine curve

Study group on the Fargues-Fontaine curve 2024/2025

Work group on condensed mathematics

Condensed mathematics 2022

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.

Scope of the seminars is to introduce base concepts in the theory developed in recent years by Fabrizio Andreatta and Adrian Iovita among the integral theory of authomorphic forms and to show some applications in the 1-dimensional case. Talks will be given in English. Schedule:
09/10/2020 Introduzione ai fibrati formali con sezioni marcate
16/10/2020 Fasci di sezioni: sottomoduli tagliati da un carattere e filtrazioni naturali
23/10/2020 Connessioni sulle sezioni di un fibrato formale con sezioni marcate
30/10/2020 Modello formale dello spazio di pesi p-adico e carattere universale
6/11/2020 Spazi di moduli di curve ellittiche e sottogruppo canonico
13/11/2020 Costruzione della torre di Igusa (finita)
20/11/2020 Costruzione dei fasci modulari sulla torre di Igusa, 1
27/11/2020 Costruzione dei fasci modulari sulla torre di Igusa, 2

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.

In the theory of algebraic curves, a prominent role is played by uniformization, i.e., the description of a curve as the quotient of an open dense subset of the projective line by the action of a Schottky group. All complex algebraic curves admit uniformization, as well as some p-adic curves, called Mumford curves. In this talk, I present a construction of universal Mumford curves, analytic spaces that parametrize both archimedean and non-archimedean uniformizable curves of a fixed genus. This construction relies on the existence of suitable moduli space for marked Schottky groups, that can be achieved using the theory of Berkovich spaces over rings of integers of number fields. In a second part, I explain how we can derive topological properties of Schottky spaces and universal Mumford curves by comparing them with two classical objects: the Culler-Vogtmann outer space and the moduli space of tropical curves. This is joint work with Jérôme Poineau.

May 6, 2019 - room SR701 - 14:15 - Giacomo Graziani - Tate's uniformisation: from complex to p-adic. I. May 13, 2019 - room 2BC60 - 14:30 - Giacomo Graziani - Tate's uniformisation: from complex to p-adic. II.

Katz’s definition of modular forms and the p-adic version

Wednesday October 12, 2016 - room SRVII - time 14:30 - Matteo Longo Friday October 21, 2016 - room 2BC30 - time 14:30 - Giacomo Graziani Friday November 4, 2016 - room 2BC30 - time 14:30 - Giacomo Graziani Friday November 11, 2016 - room 2BC30 - time 14:30 - Giacomo Graziani Friday November 18, 2016 - room 2BC30 - time 14:30 - Giacomo Graziani Friday December 2, 2016 - room 2BC30 - time 14:30 - Davide Barco Friday January 13, 2017 - room 2BC30 - time 14:30 - Giacomo Graziani

p-adic seminar: Connections on Berkovich curves

Wednesday November 23, 2016 - room 1BC45 - time 15:00 - Velibor Bojkovic Wednesday November 30, 2016 - room 2AB45 - time 15:00 - Velibor Bojkovic Wednesday December 7, 2016 - room 2AB45 - time 15:00 - Velibor Bojkovic Wednesday December 21, 2016 - room 2AB45 - time 15:00 - Velibor Bojkovic Wednesday January 25, 2017 - room 2AB45 - time 14:30 - Velibor Bojkovic Thursday February 2, 2017 - room 2AB40 - time 14:30 - Velibor Bojkovic Wednesday February 8, 2017 - room 2AB45 - time 14:30 - Velibor Bojkovic Thursday March 2, 2017 - room 1BC45 - time 14:30 - Velibor Bojkovic Thursday March 9, 2017 - room 2BC30 - time 14:30 - Velibor Bojkovic Wednesday March 15, 2017 - room SRIV - time 14:30 - Francesco Baldassarri -"Berkovich skeleta, norms on differentials and degenerations of algebraic varieties" Wednesday May 3, 2017 - room SRVII - time 14:30 - Velibor Bojkovic - "Ramification properties of finite morphisms of Berkovich curves.I" Wednesday May 10, 2017 - room SRVII - time 14:00 - Stafano Urbinati - "Valuative trees and birational geometry" Wednesday May 10, 2017 - room SRVII - time 15:00 - Velibor Bojkovic - "Ramification properties of finite morphisms of Berkovich curves. II" Wednesday May 24, 2017 - room SRVII - time 15:00 - Velibor Bojkovic Wednesday June 7, 2017 - room 2AB40 - time 14:00 - Stefano Urbinati - "The valuative tree"