Geodesics And Geometric-ARithmetic INtersections

Project Information

GAGARIN

Grant agreement ID: 101076941

DOI 10.3030/101076941

EC signature date 16 February 2023

Start date 1 May 2023

End date 30 April 2028

Funded under

• European Research Council (ERC)

Total cost € 1 500 000,00

EU contribution € 1 500 000,00

Coordinated by

UNIVERSITEIT LEIDEN
Netherlands

Objective

This project will develop several aspects of a theory of real multiplication (RM), seeking to be a counterpart of the theory of complex multiplication (CM) discovered in the 19th century. Classical CM theory is famed for its beauty and elegance, and is important in a variety of contexts. For instance:

(1) in the classical era, it arose in the context of explicit class field theory. This feature is the subject of Kronecker's Jugendtraum and Hilbert's 12th problem,
(2) in the modern era, it has been instrumental in proving known cases of the Birch-Swinnerton-Dyer conjecture, notably the results of Gross-Zagier which are a main theme of this proposal,
(3) it has been used in elliptic and hyperelliptic curve cryptography, in cryptosystems based on supersingular isogeny graphs, one of the front runners for a secure post-quantum international standard.

The objectives are to develop analytic, computational, and geometric aspects of such an RM theory, and address the full scope of these features. The theory is based on the notion of arithmetic intersections of geodesics, and this project gives a new approach towards RM theory based on a notion of p-adic weak harmonic Maass forms, and p-adic height pairings of geodesics attached to real quadratic fields.

Emphasis will lie on analytic aspects (p-adic Borcherds lifts and p-adic mock modular forms), computational aspects (development of user-friendly software for computations in RM theory), and geometric aspects (RM cycles on Shimura curves, and applications to the Birch-Swinnerton-Dyer conjecture).

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.

• natural sciences › computer and information sciences › software
• natural sciences › computer and information sciences › computer security › cryptography

You need to log in or register to use this function

Keywords

• Modular forms
• complex multiplication
• p-adic methods
• elliptic curves

Programme(s)

• HORIZON.1.1 - European Research Council (ERC) Main Programme

Topic(s)

• ERC-2022-STG - ERC STARTING GRANTS

Call for proposal

ERC-2022-STG

Funding Scheme

HORIZON-ERC - HORIZON ERC Grants

Host institution

UNIVERSITEIT LEIDEN

• Net EU contribution: € 1 500 000,00
• Address: RAPENBURG 70 ; 2311 EZ Leiden ; Netherlands
• Activity type: Higher or Secondary Education Establishments
• Total cost: € 1 500 000,00

Beneficiaries (1)

UNIVERSITEIT LEIDEN

Netherlands

• Net EU contribution: € 1 500 000,00
• Address: RAPENBURG 70 ; 2311 EZ Leiden
• Activity type: Higher or Secondary Education Establishments
• Total cost: € 1 500 000,00