GEMS: Geometric structures, moduli spaces, and dualities

GEMS is a ‘coordinated project’ , funded by the Spanish Ministry of Science, Innovation and Universities, consisting of two subprojects, DUKES (Dualities, K-stability and special holonomy) and HISMO (Higgs bundles, integrable systems and moment-map equations). DUKES and HISMO are unified through joint objectives centered around moduli spaces, which are central objects in geometric classification problems.

DUKES will make progress in fundamental problems in differential and algebraic geometry, combining generalised and higher geometry, geometric analysis, and birational geometry. The unifying theme is the theory of moduli spaces, both in its more classical algebraic-geometric form and in its analytical and gauge-theoretic aspects, as well as in its connections with higher structures and theoretical physics. Key topics include special holonomy, moduli spaces, the study of canonical Kähler metrics in both their algebraic and analytic versions and the mathematical study of dualities in string theory (mirror symmetry and holography). New directions are explored in special holonomy with and without torsion, generalised geometry and higher gauge theory, as well as constructions of moduli spaces via computational algebra, K-stability, uniqueness of KählerYangMills equations, and the study of dualities: CalabiYau/hyperKähler mirror symmetry, Langlands duality, and the AdS/CFT correspondence, combining moduli-space theory, vertex algebras and exceptional geometry.

HISMO focuses on the theory of Higgs bundles, higher Teichmüller theory, generalizations of the Hitchin system and Langlands duality and mirror symmetry, non-commutative integrable systems, supergeometry, and moment-map equations in gauge theories and canonical parametrised theories. HISMO focuses on the topology of moduli spaces of Higgs bundles for non-compact real Lie groups, multiplicative and cyclic Higgs bundles associated with Vinberg pairs, Langlands duality, moduli spaces of coherent sheaves in supergeometry, non-commutative integrable systems, quasi-Hamiltonian algebras, double Poisson or double CourantDorfman algebras, dimensional reduction and toric varieties, and moduli spaces of principal bundles with non -reductive structure group.

DUKES and HISMO are supported by Ministerio de Ciencia, Innovación y Universidades of Spain with grant numbers PID2025-174260NB-C21 and PID2025-174260NB-C22, respectively.

DUKES Team

  • Mario Garcia-Fernandez (ICMAT-CSIC; co-IP)
  • Jesús Martínez-García (Universidad Autónoma de Madrid; co-IP)
  • Andoni de Arriba de la Hera (Universidad Nacional de Educación a Distancia)
  • Emilio Franco (ICMAT-Universidad Autónoma de Madrid)
  • Román Ahumada Giallanela (ICMAT-Universidad Autónoma de Madrid)
  • Izar Alonso Lorenzo (ICMAT-CSIC)
  • Giuseppe Barbaro (ICMAT-CSIC)
  • Nestor Blazquez Hernán-Gómez (ICMAT-CSIC)
  • Ivan Cheltsov (University of Edinburgh)
  • Eric Y. Chen (EPFL)
  • Jean Chessa (ENS Lyon) 
  • Jessica Claridge (University of Essex)
  • Eleonora Di Nezza (Universita Degli Studi Di Roma Tor Vergata)
  • Erroxe Etxabarri-Alberdi (Mondragon Unibersitatea)
  • Robert Hanson (Imperial College London)
  • Joshua Jackson (University of Cambridge)
  • Raúl González Molina (Universidad Politécnica de Madrid)
  • Anne-Sophie Kaloghiros (Brunel University)
  • Eveline Legendre (Université Lyon 1 – Institut Camille Jordan)
  • Alfredo Llosa Lazo (ICMAT-Universidad Autónoma de Madrid)
  • Francesco Sala (University of Pisa)
  • Adrián Santos Quiles (Northwestern University)

HISMO Team

  • Luis Álvarez Cónsul (ICMAT-CSIC; co-IP)
  • Óscar García-Prada (ICMAT; co-IP)
  • David Fernández Álvarez (Universidad Politécnica de Madrid)
  • Pablo Alvarado Seguel (ICMAT-CSIC)
  • Olivier Biquard (Sorbonne Université)
  • Brian Collier (UC Riverside)
  • Guillermo Gallego Sánchez (Freie Universitat Berlin)
  • Miguel González González (ICMAT-CSIC)
  • Peter Gothen (Universidade do Porto)
  • Tamas Hausel (IST Austria)
  • Jochen Heinloth (Universitat Duisburg-Essen)
  • Raimundo Heluani (IMPA)
  • Jacques Hurtubise (McGill University)
  • Sergio Martín Nieto (Universidad Complutense de Madrid)
  • Alejandro Plaza Gallán (ICMAT)
  • Diego Ruiz Cases (ICMAT-CSIC)
  • Lucía Sobral Torres (Universidad Complutense de Madrid)
  • Manuel Timiraos López (ICMAT-CSIC)