LGModGal · Local and global geometry of moduli spaces of p-adic Galois representations
„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“
- Период
- 2025-10-01 → 2027-09-30
- Финансиране от ЕС
- 260 348 €
- Участници
- 1
- Схема
- HORIZON-TMA-MSCA-PF-EF
Линиите свързват координатора с партньорите.
Накратко на български
Геометрията на пространствата, изградени от симетрии на полиномни уравнения (като $Y^2=X^3+X+1$), се анализира чрез алгебрична геометрия и теория на представянията. Това помага за разбирането на връзката между дискретната и непрекъснатата математика, което е важно за решаването на проблеми в теорията на числата.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Цел на проекта
The Langlands correspondence is a series of mathematical predictions describing a deep relationship betweentwo fundamental branches of mathematics: discrete mathematics, which is the basis of counting and numbertheory, and continuous mathematics, which underlies analysis. These connections are incredibly powerful and have helped solve some of the most challenging problems in mathematics, such as Fermat's Last Theorem, which remained unsolved for nearly 400 years. Despite significant advances over the past 30 years, much of this area remains unexplored. Recently, a new approach has emerged with the potential to revolutionise our understanding of the Langlands correspondence. The expectation is that this correspondence can be achieved via an interpretation of the analytic side as functions on geometric spaces which are built from basic objects on the discrete side—specifically symmetries of solutions to polynomial equations like Y²=X³+X+1. While it is speculated that this viewpoint will substantially simplify the problem, it is presently unclear how exactly these ideas should be implemented. A major issue is that the underlying geometry of these spaces are hard to control, rendering a precise interpretation as functions difficult.My research has hinted that, through innovative combinations of techniques from algebraic geometry and representation theory, taming this geometry is within reach. In this project I will develop these ideas to produce a general framework which controls these spaces. Consequently, foundational results in the Langlands correspondence, currently limited to dimension 2, will be developed in higher dimensions, making inroads into one of the most important and enduring problems of modern number theory.
Оригинален текст от CORDIS (на английски).
Участници
- QUEEN MARY UNIVERSITY OF LONDON · LONDONКоординаторОбединеното кралство
Връзки
- Виж в CORDIS
- DOI: 10.3030/101204730
- https://ec.europa.eu/research/participants/documents/downloadPublic?documentIds=080166e52c5eefae&appId=PPGMS
Данни: CORDIS, © Европейски съюз