Maths frontiers explored by Europe's top researchers

Leading European and British mathematicians explored cutting-edge problems at a landmark University of Essex event.

The researchers attended AGGITatE 2025, an international conference exploring advances in group theory and representation theory.

Groups are sophisticated objects that capture properties of symmetry, such as how many times we can flip and rotate a polygon to put it back in place.

Group theory is pervasive to many areas of science and engineering, modelling a diverse array of problems, from the interaction of subatomic particles, to solving a Rubik’s cube.
Representation theory studies the different ways groups can act on multi-dimensional spaces.

Over three days, delegates shared breakthroughs on symmetry, algebra, and geometry - including solutions to long-standing problems, whilst enjoying the sun on the Colchester Campus.

'Major developments'

It featured 18 talks, a lively social programme, and support from the London Mathematical Society, the Heilbronn Institute, and the Isaac Newton Institute (INI).

Organised by the University’s School of Mathematics, Statistics and Actuarial Science (SMSAS) more than 40 researchers focussed on representations of symmetric groups and related algebras, local-global results for groups and related objects and cohomology.

The attendees showcased a range of career stages, with many early-career researchers, in particular PhD students.

Dr Alastair Litterick, organiser and Senior Lecturer in SMSAS, said: "It’s been great hearing about major developments from some of the brightest minds in the area, and it’s fantastic to have such a vibrant crowd of PhD students, early-career researchers and high-profile visit us on campus."

Co-organising PhD student Harvey Sykes echoed Dr Litterick’s thoughts and said: "AGGITatE 2025 offered me and many PhD students a unique opportunity to engage with leading figures in modular representation theory at a time of remarkable progress in the field."

Delegates heard about major advances, including:

•A solution to a long-standing local-global conjecture by Associate Professor Eugenio Giannelli from the University of Florence.
•A new proof of the 2002 Isaacs–Navarro conjecture by Lucas Ruhstorfer, of the University of Wuppertal.
•Professor John Greenlees, from the University of Warwick, presented research on singularity categories
•Professor Radha Kessar, from the University of Manchester, Associate Professor Carolina Vallejo Rodriguez, University of Florence, and Professor Markus Linckelmann, City St George’s, discussed developments following the solution to the McKay conjecture.

Cross-disciplinary

The AGGITatE conference series is designed to broaden academic horizons, especially for early-career researchers, by encouraging cross-disciplinary exchange.

First held at Essex in 2022, AGGITatE has since covered topics ranging from algebraic groups and algebraic geometry to the Cremona group and moduli of varieties.

This year’s organising team included Harvey Sykes, Dr Jay Taylor, Dr Litterick, and Dr Jesús Martínez-García.

Organiser Dr Martínez-García added: "After four consecutive editions, AGGITatE is now a staple in the annual circuit of UK conferences in algebra and geometry, and an important addition to our School’s REF 2029 Environment strategy.

"Preparations are underway for the 2026 edition, which will be part of an INI-funded month-long research programme at Essex with over 30 researchers from around the world at any one time."