Simple fusion systems and linking systems

Información del proyecto

FusionSystems

Identificador del acuerdo de subvención: 707758

DOI

10.3030/707758

Proyecto finalizado el 2 Agosto 2017

Fecha de la firma de la CE 24 Febrero 2016

Fecha de inicio 3 Agosto 2016

Fecha de finalización 2 Agosto 2018

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 195 454,80

Aportación de la UE

€ 195 454,80

Coordinado por

THE UNIVERSITY COURT OF THE UNIVERSITY OF ABERDEEN
United Kingdom

Objetivo

The classification of finite simple groups is often regarded as one of the major mathematical achievements of the 20th century. Its importance lies not only in the fundamental result, but also in the methodology and conceptual framework developed for its proof. Most intriguingly, it turned out that the structure of a finite group is closely connected to the structure of the p-local subgroups, i.e. the normalizers of non-trivial p-subgroups, for a suitably chosen prime p. Of particular importance is the prime 2. Even though the proof of the classification of finite simple groups is insightful in its major conceptual approach, it is extremely long and difficult in its details. Thus, it would be of great interest to obtain a simplified proof. Moreover, to gain the maximum benefit from the methods of the proof of the classification, it is highly desirable to work in a more general context which in particular allows also for applications in the modular representation theory of finite groups. Saturated fusion systems provide a conceptual framework for this and connect to important questions in homotopy theory. A program to find a new and better proof of the classification of finite simple groups through a classification of simple fusion systems at the prime 2 has been recently outlined by Aschbacher. Two parts of our proposal concern classification problems for fusion systems. Their significance lies not only in completing important cases in Aschbacher's program, but also in giving new insight into the relative abundance of exotic examples, i.e. fusion systems not induced by any finite group. In the third part we attack a major problem in the algebraic theory of fusion systems by defining an analogue in fusion systems of centralizers of subgroups of finite groups. This will simultaneously facilitate a classification of fusion systems in the spirit of Aschbacher's program, and lead to a combinatorial understanding of maps between classifying spaces of fusion systems.

Ámbito científico (EuroSciVoc)

• humanidades › historia y arqueología › historia
• ciencias naturales › matemáticas › matemáticas puras › topología
• ciencias naturales › matemáticas › matemáticas puras › álgebra
• ciencias naturales › matemáticas › matemáticas puras › geometría
• ciencias naturales › matemáticas › matemáticas puras › aritmética › números primos

Palabras clave

• Finite group theory
• fusion systems
• related homological algebra and homotopy theory

Programa(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions PROGRAMA PRINCIPAL
  
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
  

Tema(s)

• MSCA-IF-2015-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF)
  

Régimen de financiación

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Convocatoria de propuestas

H2020-MSCA-IF-2015

Coordinador

THE UNIVERSITY COURT OF THE UNIVERSITY OF ABERDEEN

• Aportación neta de la UEn: € 195 454,80
• Dirección: KING'S COLLEGE REGENT WALK ; AB24 3FX Aberdeen ; Reino Unido
• Región: Scotland › North Eastern Scotland › Aberdeen City and Aberdeenshire
• Tipo de actividad: Higher or Secondary Education Establishments
• Coste total: € 195 454,80