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Hypatia Graduate Summer School 2025

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Advanced course / School
From June 16, 2025
to June 19, 2025

Venue: CRM Auditorium

Registration: will open by January 2025 (100% onsite)

Included: the attendance to all the activities during the school, coffee breaks, lunches, and catering during the colloquium at IEC

*Attending the colloquium (open for everybody) is free but registration is compulsory by filling out the following:

HYPATIA COLLOQUIUM FORM FOR ATTENDANCE (TBP)

*Registration for the col.loquium is not necessary for those participating at Hyaptia School. They will be added to the attendance list.

Registration deadline 02 / 06 / 2025

HYPATIA CHRONICLE & PHOTOS

Declaration of intent

This summer school series aims at training their participants in key strategic problems in mathematics and their applications, with the core idea that theory and applications strengthen each other. The school is focused in training of young researchers whilst opening new fields for senior ones.

The Hypatia Graduate Summer School will consist in two keynote courses on subjects of exceptional promise and scientific importance delivered by highly distinguished speakers in the area plus a high-level colloquium on a complementary subject.

The Hypatia Graduate Summer School will be developed in an informal atmosphere based on discussions, exchange of ideas and critical analysis of results. Moreover, to honour its namesake, it is committed to work under a friendly gender perspective that highlights the role of women in mathematics and encourages and helps the participation and promotion of young female researchers at a professional level.

Previous editions

Hypatia 2024

Hypatia 2023

Hypatia 2022

Lecturers

Website

Henri Darmon

McGill Universit

Henri is a distinguished professor at McGill University, specializing in algebraic number theory. His research focuses on elliptic curves, modular forms, and associated L-functions, which are central topics in modern number theory. He has authored over 80 papers in top journals including Annals of Math., Journal AMS, Inventiones Math. or Duke Math. J. He is a fellow of both the Canadian and the American Mathematical Societies and has received numerous accolades. He is known for his excellence in graduate teaching and supervision. Darmon’s teaching style is lauded for its clarity, and his seminars draw international attention, inspiring both students and colleagues alike.

Website

Victor Rotger

Universitat Politècnica de Catalunya

Victor is a professor at Universitat Politècnica de Catalunya and ICREA Academia researcher. His academic achievements include an ERC Consolidator Grant. Victor’s research focuses on deep questions in number theory related to the Birch and Swinnerton-Dyer conjecture, Bloch-Kato conjecture, Stark-Heegner points, and Euler systems, among others. He has also built new research directions on Euler systems, the p-adic Kudla program and the arithmetic of Shimura varieties. He has authored papers in top journal such as Journal AMS, Journal EMS, Forum Math Pi or Ann. Sci. Éc. Norm. Sup. In addition, he has held visiting research positions at prestigious institutions like McGill University, the Tata Institute, and Humboldt University.

Website

Özlem Imamoḡlu

ETH Zurich

Özlem is a professor at ETH Zurich. Her work focuses on modular forms, automorphic forms, and arithmetic geometry. She has contributed significantly to understanding the connections between number theory and geometry, particularly through the study of modular curves and modular functions. She has authored papers in top journals such as Annals of Math., Duke Math J. , Journal of EMS or Crelle’s Journal. In addition to her research, Özlem is deeply committed to teaching and mentoring at ETH Zurich, where she also participates in organizing seminars and academic events.

Website

Paloma Bengoechea

Universitat de Barcelona

Paloma is a Ramon y Cajal researcher at the Universitat de Barcelona. She obtained her PhD at Université Paris VI supervised by Don Zagier and Pilar Bayer. She held a postdoctoral position at the University of York and obtained the prestigious Ambizione grant from the Swiss National Foundation (SNF) and became a Senior Research Assistant at ETH Zurich. Her mathematical work addresses different areas of number theory, more particularly the interplays between the theory of modular forms and the areas of diophantine approximation and diophantine equations. She has published articles in top journals such as Math. Annalen, IMRN or Trans. AMS.

COURSES

COURSE 1 | Rational points on elliptic curves and deformations of modular forms

Lecturers: Henri Darmon (McGill University) and Victor Rotger (Universitat Politècnica de Catalunya)

Abstract:

Finding explicit constructions of algebraic points on elliptic curves is one of the main questions raised by the celebrated Birch and Swinnerton-Dyer conjecture. Heegner points, which are defined over ring class fields of imaginary quadratic fields and emerge naturally from the theory of complex multiplication and the modularity of elliptic curves, are a prototype for the kind of construction one would like to dispose of in a broader range of scenarios. In their seminal work on heights and derivatives of $L$-series, Gross and Zagier relate the heights of Heegner points to the fourier coefficients of derivatives of complex analytic families of non-holomorphic Eisenstein series. This lecture series aims to explore a converse of this approach, in which the study of deformations of certain modular generating series, particularly $p$-adic ones, seem to predict explicit constructions of algebraic points in settings that go squarely beyond the theory of complex multiplication.

COURSE 2 | Periods of modular functions over closed geodesics.

Lecturers: Özlem Imamoḡlu (ETH Zurich) and Paloma Bengoechea (Universitat de Barcelona)

Abstract:

The theory of complex multiplication has a long and celebrated history. In particular it tells that the values of the Klein’s modular invariant at the imaginary quadratic irrationals, the singular moduli, are algebraic integers. In this series of talks we define “values” of modular functions at real quadratic irrationals in terms of their cycle integrals over geodesics on the modular surface. We then study various properties of these numbers, some of them are now proven, others still conjectural.

HYPATIA COLLOQUIUM

TBP

TBP

TBP

 

*If you wish to attend the HYPATIA Colloquium please confirm your attendance by filling out the following form:

HYPATIA COLLOQUIUM FORM FOR ATTENDANCE (TBP)

ABSTRACT

TBP

 

Website

Schedule

TBP

REGISTRATION AND ACCOMMODATION GRANTS

In order to increase the number of young researchers participating in this activity, the CRM offers grants to cover the registration and lodging expenses.

To apply, you must complete the registration process; please go to SIGN IN, choose the General registration option and indicate in the OTHERS section which grant options you wish to apply for; you will be asked to attach your CV. Please click on the Reservation option before finishing the process.

 

Application deadline for grants is March 30, 2025
Resolutions will be sent by April 15. 2025

 

*Registration covers the attendance to all the activities during the school, coffee breaks, lunches, including the catering  at IEC

LIST OF PARTICIPANTS

Name Institution

INVOICE/PAYMENT INFORMATION

IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.

UPF | UB | UPC | UAB

*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to comptabilitat@crm.cat with your name and the institution internal reference number that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed.

Paying by credit card

IF YOU PAY VIA CREDIT CARD but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to comptabilitat@crm.cat providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).

Lodging information

ON-CAMPUS AND BELLATERRA

BARCELONA AND OFF-CAMPUS 

Acknowledgements

 

For inquiries about this event please send an email to crmactivitats@crm.cat

 

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