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ViaFiPoS
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Representation theory equivariant topology and Langlands duality via fixed poin...

Representation theory equivariant topology and Langlands duality via fixed point schemes We propose a three-way dictionary between representation theory of complex semisimple Lie groups, equivariant topology of affine Schubert varieties and mirror symmetry for Langlands dual Hitchin systems via the language of fixed p... see more

28/02/2031

IST AUSTRIA

2M€

Project Budget: 2M€

Equipo y fechas

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

PARTICIPATION DEPralty Sin fecha límite de participación.

Ver 6 Participantes

Financing granted El organismo HORIZON EUROPE notifico la concesión del proyecto The day 2025-07-31 We do not have the information of the call

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characteristics of the participant

Este proyecto no cuenta con búsquedas de partenariado abiertas en este momento.

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6 Participantes

IST AUSTRIA

2.50M€ | Leader

ALTER TECHNOLOGY TUV NORD

350.75K€ Participante

IMEC

550.10K€ Participante

AIRBUS DEFENCE AND SPACE SAS

678.43K€ Participante

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Project duration: 66 months Date Start: 2025-07-31
End date: 2031-02-28

Equipo y fechas

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Project Budget 2M€

participation deadline Sin fecha límite de participación.

Project description We propose a three-way dictionary between representation theory of complex semisimple Lie groups,
equivariant topology of affine Schubert varieties and mirror symmetry for Langlands dual Hitchin systems
via the language of fixed point schemes. This unified framework will yield new insights and advances
within these fields, with applications extending to other areas of mathematics and quantum physics.

We introduce big algebras, which are commutative algebras attached to representations of complex
semisimple Lie groups. We view them as commutative avatars of the representation because they bring
together a wealth of sophisticated information, including a novel ring structure on multiplicity spaces,
the weight diagram and crystal structure.

We geometrize the study of equivariant cohomologies of various varieties with group action by
representing them as rings of functions of certain fixed point schemes of the group action. Adopting this
perspective, we propose novel scheme-theoretic counterparts to several fundamental constructions in
algebraic topology, such as equivariant integration, Hodge and Lefschetz theory. For affine Schubert
varieties, these counterparts offer an alternative topological approach to understanding big algebras.

Due to our central observation that the Hitchin integrable system on various Lagrangians can be modelled
by the spectrum of equivariant cohomology and big algebras, we propose a host of computational tests
of conjectured mirror branes of Kapustin–Witten in Langlands dual Hitchin systems.

We explore several applications, including polynomial relationships between quantum numbers in baryon
multiplets; a big algebra approach to Kashiwara’s conjecture on affine crystals; compatibility with Langlands
duality, endoscopy, transfer and character formulas in the relative Langlands program; geometrization of
various q = −1 phenomena and cyclic sieving in algebraic combinatorics.

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ViaFiPoS financed

6 Participantes

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ViaFiPoS
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