GEOMVAP
Geometry of Varieties and Applications
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About us
About us
We are a leading and internationally recognized research group working on Symplectic and Poisson geometry, Singularities of Algebraic Varieties and their applications, viewing problems from a variety of different perspectives. The group has a long tradition working on various different interfaces of algebra, geometry, topology and mathematical physics. In the last decade, we have become active contributors in interdisciplinary science and we focus both on a theoretical point of view and on the transversal applications to several disciplines including several aspects of Algebraic Statistics, Phylogenetics and featuring important contributions in Robotics and the mathematical foundations of computer science. In recent years, we have also obtained outstanding contributions to Fluid Dynamics, Celestial Mechanics and applications to Physics.
Research Topics
Research Topics
Our group works on topological and differentiable manifolds, algebraic varieties, and their applications, approaching problems from a broad range of complementary perspectives. The group has a long-standing tradition of research at the interfaces of algebra, geometry, and topology.
Over the past decade, we have become active contributors to interdisciplinary science. Our research program combines a strong theoretical focus with transversal applications across several disciplines, including Robotics, Machine Learning, Physics, Fluid Dynamics, and Celestial Mechanics.
Our research is organized into six closely related research lines that interact in a dynamic manner. The first two lines are primarily theoretical, while the remaining four are interdisciplinary in nature. Most members of the group contribute to more than one research line, reflecting the genuinely multidisciplinary character of our work.
Below, we include a diagram illustrating the different research lines and their members.
Research lines:
SYM – Symplectic and Poisson Geometry
AGE – Algebraic Geometry and Commutative Algebra
PHY – Applications to Physics
BIO – Applications to Biology
ROB – Applications to Robotics and Artificial Intelligence
DYN – Applications to Fluid Dynamics and Celestial Mechanics
Each research line has a designated coordinator, highlighted in the first column below. Together, the coordinators form the Steering Committee of the research group.
Funding
Funding
The group has enjoyed continuous and competitive funding for over two decades, reflecting both scientific excellence and long-term coherence. We are funded by the Generalitat de Catalunya through AGAUR’s Programme for the Support of Research Group Activities, having been awarded support in every call over the last 20 years:
2005 SGR-00557, 2009 SGR-1284, 2014 SGR-634, 2017 SGR-932, 2021 SGR-00603
We have maintained a sustained presence in national competitive funding schemes of the Spanish Ministry of Science and Universities, securing a continuous sequence of projects:
PID2019-103849GB-I00, PGC2018-098265-B-C33, MTM2014-54855-P, DGICYT PS90-0069, PB93-0790, PB96-0234, BFM2000-0799, BFM2003-06001, BFM2003-02914, DGI MTM2006-14234, MTM2012-38122-C03/FEDER.
Our current projects are:
Interacciones de Geometría con Álgebra y Aplicaciones (INTERGAP) PID2023-146936NB-I00 (PIs: Eva Miranda and Josep Alvarez).
Cuantización de Estructuras de Kähler generalizadas CNS2023-144898 (PI: Marco Gualtieri).
Espacios de Moduli y Cuantización PID2024-155686NB-I00 (PI: Marta Mazzocco).
Invariantes de Hodge de Singularidades Algebraicas PID2024-159412NA-I00 (PI: Guillem Blanco).
Celestial Mechanics, Hydrodynamics, and Turing Machines (AQUACELL) AEI-DFG project, PCI2024-155042.(PI: Eva Miranda).
We also benefit from the BBVA Foundation projects:
Computational, dynamical and geometrical complexity in fluid dynamics (COMPLEXFLUIDS) (PI: Eva Miranda).
Start-up grant José Luis Rubio de Francia prize (PI: Guillem Blanco).
International projects:
Celestial Mechanics, Hydrodynamics, and Turing Machines, Himmelsmechanik, Hydrodynamik und Turing-Maschinen (AQUACELL) AEI-DFG project, PCI2024-155042.(PI: Eva Miranda, Kai Cieliebak and Daniel Peralta-Salas).
Poisson Geometry, theory and applications FAPERJ(Brazil)CNE-E-26/204.097/2024 (PI: Alejandro Cabrera).
Leverhulme Trust Research Project Grant RPG-2021-047 (PI: Marta Mazzocco)
Cluster algebras, Teichmüller theory and Macdonald polynomials, Research Grant, EPSRC (PI: Marta Mazzocco)
2024-2029 NSERC Discovery Grant RGPIN-2024-05764 (PI: Marco Gualtieri)
2018-2024 NSERC Discovery grant (PI: Marco Gualtieri)
Prizes
Prizes
We present here a list of prestigious prizes and honours awarded to members of the group, as well as to doctoral and predoctoral researchers under our supervision:
Eva Miranda Named 2027 Uhlenbeck Lecturer at the Institute of Advanced Studies in Princeton
Guillem Blanco Rubio de Francia Prize 2024.
GEOMVAP research group 2024 UPC Ciència Oberta Prize (second prize).
Eva Miranda Nachdiplom Lecturer 2025 at ETHZ
Eva Miranda Gauss Professor 2025 at the Niedersächsische Akademie der Wissenschaften zu Göttingen
Eva Miranda Stem Woman Award, 2024
Eva Miranda Premi Ciutat de Sant Cugat 2024
Marta Mazzocco EMS distinguished Speaker 2024.
Maria Alberich and Eva Miranda, 50 Dones UPC 2023
Eva Miranda London Mathematical Society Hardy Lecturer 2023
Eva Miranda François Deruyts Prize 2022
Eva Miranda Friedrich Wilhelm Bessel-Forschungspreis 2022
Eva Miranda ICREA Academia Professor (2022-2026)
Marco Gualtieri 2021 CMS Cathleen Sunge Morawetz Prize.
Eva Miranda Chair d'Excellence de la Fondation Sciences Mathématiques de Paris (2017-2018)
Eva Miranda ICREA Academia Professor (2016-2021)
Prizes for doctoral theses defended within the research group:
Thesis by Guillem Blanco (supervisors: M. Alberich and J. Alvarez): Premi Extraordinari de Doctorat 2022, IEC–Assumpció Català i Poch Prize 2022, Vicent Caselles Prize 2022, Rubio de Francia Prize 2024.
Thesis by Robert Cardona (supervisor: E. Miranda): Premi Extraordinari de Doctorat 2023, IEC–Assumpció Català i Poch Prize 2025, Vicent Caselles Prize 2023.
Thesis by Franco Coltraro (supervisors: M. Alberich and J. Amorós): IEC–Isabel de Portugal Trabal i Tallada Prize 2024.
Évariste Galois Prize for the best Master’s theses (TFM):
P. Nicolás 2024 (supervisor: E. Miranda), P. López 2025 (supervisor: J. Alvarez); Honourable Mention for R. Gómez 2024 (supervisors: M. Alberich and J. Alvarez).
Emmy Noether Prize for the best Bachelor’s theses (TFG):
Honourable Mentions for P. López 2024 (supervisors: E. Quinlan and J. Alvarez), O. Baeza 2025 (supervisors: G. Blanco and J. Alvarez), P. Mir 2022 (supervisor: E. Miranda), R. Cardona 2019 (supervisor: E. Miranda).
Other prizes for Master’s and Bachelor’s theses:
Wolfram Award: I. Ramos 2024 (supervisors: E. Miranda, A. González-Prieto, D. Peralta-Salas), Staff Pick by the Wolfram Community.
Arquimedes prize: Honourable Mention J. Fontana 2022 (supervisors: E. Miranda, D. Peralta-Salas).
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