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Description
An IMPA - ICTP Online School -  held in Spanish and Portuguese

The AGRA series of summer schools (Santiago de Chile, 2012; Cusco, 2015; Córdoba, 2018) has as its goal to foster the development of number theory in Latin America: it provides a formative experience for young researchers, and it also brings together senior and mid-career mathematicians working in the field. The primary languages for this event are going to be Spanish and Portugese.


Description:
The target audience of AGRA includes undergraduate students, graduate students and young researchers with a serious interest in number theory and neighboring fields. The AGRA IV has been divided into two parts: part 1 is this online school in August 2021, while part 2 is preliminarily scheduled to take place in the first semester of 2022 in Cabo Frio, Brazil. The adjoined list of topics is representative of the two parts. The AGRA series has traditionally been held in Spanish but, this time, Spanish and Portuguese will share a role as primary languages of the school. Part 1 will consist of 4 minicourses delivered by a pool of distinguished mathematicians, followed by tutorials and problem sessions.
 
Topics:
• Arithmetic geometry
• Group approximations
• Arithmetic combinatorics
• Mahler measure
• Model theory
• Square-tiled surfaces
• Analytic methods in number theory


Programme:

Minicourse 1:
Introducción al análisis de Fourier de orden superior
(Introduction to higher order Fourier analysis)
• Julia Wolf (Cambridge, UK)
• Pablo Candela (UAM / ICMAT, Spain)

Syllabus


Minicourse 2:
Superficies racionales sobre un cuerpo
(Rational surfaces over a field)
• Tony Varilly-Alvarado (Rice, USA)
• Damiano Testa (Warwick, UK)

Syllabus


Minicourse 3:
Combinatória de superfícies quadriculadas e geometria de espaços de módulos
(Combinatorics of lattice surfaces and geometry of moduli spaces)
• Carlos Matheus (École Polytechnique / CNRS, France)
• Vincent Delecroix (Bordeaux / CNRS, France)

Syllabus


Minicourse 4:
Normativa para Ecuaciones diofantinas con pocas soluciones
(Diophantine equations with few solutions)
• Hector Pasten (PUC, Chile)

Syllabus


Registration:  There is no registration fee


 

Material

AGRA IV (Arithmetic, Groups and Analysis) - Part I (smr 3617)
Go to day
  • Monday, 16 August 2021
    • 14:45 - 15:00 OPENING: ALL TIMES BELOW ARE ITALIAN TIME ZONE (GMT +2) 
      WELCOME by the Organizing Committee

M. Belolipetsky (IMPA, Brazil)
E. Carneiro (ICTP, Italy)
D. Dimitrov (UNESP, Brazil)
H. Helfgott (Goettingen, Germany / CNRS, France)
M. Lalin (Montreal, Canada)
S. Lima (IMPA, Brazil)
Y. Lima (UFC, Brazil)
A. Pacetti (Cordoba, Argentina)
P. Pino (UFF, Brazil)
F. Rodriguez-Villegas (ICTP, Italy)
    • 15:00 - 22:00 SESSION 1 - MAIN LECTURES
      • 15:00 MINICOURSE 1 - Introduccion al analisis de Fourier de orden superior 50'
        Speaker: Julia Wolf and Pablo Candela (Cambridge, UK and UAM/icmat, Spain)
        Material: Exercises Slides Solutions of Exercises 1 Solutions of Exercises 2
      • 15:50 Coffee break 10'
      • 16:00 MINICOURSE 2 - Superficies racionales sobre un cuerpo 50'
        Speaker: Damiano Testa and Tony Varilly-Alvarado (Warwick, UK and Rice, USA)
        Material: Lecture Notes Slides 1 Slides 2 Slides 3 Slides 4 Slides 5
      • 16:50 Coffee break 10'
      • 17:00 MINICOURSE 3 - Combinatoria de superficies quadriculadas e geometria de espacos de modulos 50'
        Speaker: Carlos Matheus and Vincent Delecroix (Ecole Polytechnique/CNRS, France and Bordeaux/CNRS, France)
        Material: Lecture Notes Sage code.ipynb Sage notes Slides 1 Slides 2 Slides 3 Slides 4 Slides 5
      • 17:50 Coffee break 10'
      • 18:00 MINICOURSE 4 - Ecuaciones diofantinas con pocas soluciones 50'
        Speaker: Hector Pasten (PUC, Chile)
        Material: Exercises Lecture Notes
      • 19:00 SESSION 1 - TUTORIALS 3h0' 
        Rooms (one for each minicourse) will be open for discussions between the students everyday from 7.00 to 10.00 pm (CEST)
2.00 to 5.00 pm (Rio de Janeiro time)

Minicourse 2
Tutor:  Tony VARILLY-ALVARADO (Rice University, USA)
will lead the session from 8.30 to 10.00 pm (CEST)
3.30 to 5.00 pm (Rio de Janeiro time)

Minicourse 3
Quentin GENDRON (CIMAT, Mexico)
will lead the session from 7.30 to 8.30 pm (CEST)
2.30 to 3.30 pm (Rio de Janeiro time)

Minicourse 4
Tutor:  Jerson CARO (PUC, Chile)
will lead the session from 8.30 to 9.30 pm (CEST)
3.30 to 4.30 pm (Rio de Janeiro time)
  • Tuesday, 17 August 2021
    • 15:00 - 22:00 SESSION 2 - MAIN LECTURES 
      Exact repetition of the first day for the Main Lectures
      • 19:00 SESSION 2 - TUTORIALS 3h0' 
        Rooms (one for each minicourse) will be open for discussions between the students everyday from 7.00 to 10.00 pm (CEST)
2.00 to 5.00 pm (Rio de Janeiro time)

Minicourse 3
Tutor:  Quentin GENDRON (CIMAT, Mexico)
will lead the session from 7.30 to 8.30 pm (CEST)
2.30 to 3.30 pm (Rio de Janeiro time)

Minicourse 4
Tutor:  Jerson CARO (PUC, Chile)
will lead the session from 8.30 to 9.30 pm (CEST)
3.30 to 4.30 pm (Rio de Janeiro time)
  • Wednesday, 18 August 2021
    • 15:00 - 22:00 SESSION 3 - MAIN LECTURES 
      Exact repetition of the first day for the Main Lectures
      • 19:00 SESSION 3 - TUTORIALS 3h0' 
        Rooms (one for each minicourse) will be open for discussions between the students everyday from 7.00 to 10.00 pm (CEST)
2.00 to 5.00 pm (Rio de Janeiro time)

Minicourse 1
Tutor:  Diego GONZALEZ (Alfred Renyi Institute of Mathematics, Hungary)
will lead the session from 7.30 to 9.00 pm (CEST)
2.30 to 4.00 pm (Rio de Janeiro time)

Minicourse 2
Tutor:  Tony VARILLY-ALVARADO (Rice University, USA)
will lead the session from 8.30 to 10.00 pm (CEST)
3.30 to 5.00 pm (Rio de Janeiro time)

Minicourse 3
Quentin GENDRON (CIMAT, Mexico)
will lead the session from 7.30 to 8.30 pm (CEST)
2.30 to 3.30 pm (Rio de Janeiro time)

Minicourse 4
Tutor:  Jerson CARO (PUC, Chile)
will lead the session from 8.30 to 9.30 pm (CEST)
3.30 to 4.30 pm (Rio de Janeiro time)
  • Thursday, 19 August 2021
    • 15:00 - 22:00 SESSION 4 - MAIN LECTURES 
      Exact repetition of the first day for the Main Lectures
      • 19:00 SESSION 4 - TUTORIALS 3h0' 
        Rooms (one for each minicourse) will be open for discussions between the students everyday from 7.00 to 10.00 pm (CEST)
2.00 to 5.00 pm (Rio de Janeiro time)

Minicourse 3
Quentin GENDRON (CIMAT, Mexico)
will lead the session from 7.30 to 8.30 pm (CEST)
2.30 to 3.30 pm (Rio de Janeiro time)

Minicourse 4
Tutor:  Jerson CARO (PUC, Chile)
will lead the session from 8.30 to 9.30 pm (CEST)
3.30 to 4.30 pm (Rio de Janeiro time)
  • Friday, 20 August 2021
    • 15:00 - 22:00 SESSION 5 - MAIN LECTURES 
      Exact repetition of the first day for the Main Lectures
      • 19:00 SESSION 5 - TUTORIALS 3h0' 
        Rooms (one for each minicourse) will be open for discussions between the students everyday from 7.00 to 10.00 pm (CEST)
2.00 to 5.00 pm (Rio de Janeiro time)

Minicourse 1
Tutor:  Diego GONZALEZ (Alfred Renyi Institute of Mathematics, Hungary)
will lead the session from 7.30 to 9.00 pm (CEST)
2.30 to 4.00 pm (Rio de Janeiro time)

Minicourse 2
Tutor:  Tony VARILLY-ALVARADO (Rice University, USA)
will lead the session from 8.30 to 10.00 pm (CEST)
3.30 to 5.00 pm (Rio de Janeiro time)

Minicourse 3
Quentin GENDRON (CIMAT, Mexico)
will lead the session from 7.30 to 8.30 pm (CEST)
2.30 to 3.30 pm (Rio de Janeiro time)
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