In Algebraic Geometry the main goal is to study, from several points of view, the geometry of the varieties defined by polynomial equations and some attached algebraic objects, including the following topics: vector bundles defined over these varieties,  moduli spaces that classify them, complexes of sheaves and stability conditions in triangulated categories, Arakelov theory, abelian and irregular varieties, toric varieties and Hilbert schemes. From a computational point of view there is activity on Elimination  theory and effective methods applied to Algebraic Geometry.

In Commutative Algebra there is activity in the following topics: homological methods in positive characteristic, the algebraic Mellin transform, and the structure of Gorenstein rings in  any dimension. Also in the modern study of syzygies and invariants attached to free resolutions. In a more applied context, several problems related to semigroups are considered.

Members

Laura Costa Farràs

Carlos D’Andrea

Joan Elias Garcia

Ricardo García López

Martí Lahoz Vilalta

Simone Marchesi

Rosa M. Miró-Roig

Joan Carles Naranjo del Val

Martín Sombra

Santiago Zarzuela Armengou

The main research area is Arithmetic Geometry, studying the relation between geometric objects defined over number fields such as elliptic curves, abelian varieties and algebraic varieties and modular and automorphic forms. This is part of a network of  conjectures known as the Langlands Program, which includes reciprocity (or modularity) conjectures and Langlads functoriality. Another subject covers Galois representations, with applications to the Inverse Galois Problem. Other than the Langlands  Program, there is interest on the Sato-Tate conjecture, Differential Galois Theory, diophantine equations and cryptography.

Members

Paloma Bengochea

Francesc Fité

Luís Víctor Dieulefait

Xavier Guitart Morales

Artur Travesa Grau

This research direction includes several topics in Geometry, such as gauge theories, Higgs bundles, moduli spaces of geometric structures, and group actions on manifolds. It also encompasses a number of topics of Algebraic Topology, such as higher  homotopical structures, operadic calculus, and rational and p-adic homotopy. At the interface between Geometry and Topology, we study cohomological and homotopical invariants of complex manifolds, complex algebraic varieties and related geometric  spaces, such as Kähler and symplectic manifolds. Both contact and symplectic manifolds are studied from a topological and geometric point of view, as well as their connection to dynamical systems. We also carry out research in topological data analysis, an  innovative and powerful technique for applications of Topology to Neural Networks and Data Science. More information at the Topology website.

Members

Robert Cardona

Carles Casacuberta Vergés

Joana Cirici

Javier J. Gutiérrez Marín

Ignasi Mundet i Riera

We study several aspects of combinatorial geometry, algebraic combinatorics, and graph theory, and their interactions with other areas of mathematics (group theory, representation theory) and computer science (optimization, computational geometry). Our  main research lines concern the interaction between geometry and combinatorics. We study combinatorial properties of geometric objects (convex polytopes, finite point sets, hyperplane arrangements, geometric graphs), combinatorial objects motivated by  geometric instances (oriented matroids and their relation to metric graph theory), and geometric realizations of combinatorial objects (matroid polytopes, permutahedra, associahedra and their generalizations). Our research is also motivated by interactions  with algebra and algebraic graph theory. We study algebraic structures associated to combinatorial geometry and graph theory (toric ideals, automorphism groups, endomorphism monoids), and combinatorial and geometric structures arising from algebra  (Cayley graphs, reflection arrangements, cluster algebras). More info at our website: https://www.ub.edu/comb/

Members

Kolja Knauer

Arnau Padrol Sureda

Vincent Pilaud

Research pivots in a balanced way between fundamental research and the transfer of knowledge to the financial sector, articulating in two strands: the theory of stochastic partial differential equations (PDEs) and the study of continuous time models in  financial markets. Topics covered in PDEs are varied, such as probabilistic potential theory, stochastic wave equations with nonlinear coefficients, PDEs with fractional noise, and Malliavin calculus. When it comes to studying financial markets, stochastic  analysis tools are applied to address issues such as the equilibrium problem when there are investors with asymmetric information, financial bubble models, hybrid product valuation, and volatility models. . fractionated. Financial risk departments could be  the professional destination of doctoral students trained in this area.

Members

José Manuel Corcuera Valverde

David Márquez Carreras

Carles Rovira Escofet

Marta Sanz-Solé

Dynamical Systems can be considered, at present, as a way to describe evolution problems with respect to time, let them be given by ordinary or partial differential equations or by discrete transformations. Both the qualitative and the quantitative aspects of  the systems fall in this study.

In the Universitat de Barcelona dynamical systems group, we study quite diverse problems, including: Astrodynamics, Celestial Mechanics, Hamiltonian systems and holomorphic dynamics.

More information at the Dynamical Systems webpage: https://www.ub.edu/dynsys

Membres

Kostiantyn Drach

Núria Fagella Rabionet

Ernest Fontich Julià

Gerard Gómez Muntané

Marina Gonchenko

Marcel Guàrdia

Àlex Haro

Xavier Jarque i Ribera

Àngel Jorba Monte

Leticia Pardo-Simón

Joan Carles Tatjer Montaña

Arturo Vieiro Yanes

The main subjects that are considered in Mathematical Analysis are classical problems in potential and in operator theory, mainly in several complex variables, of potential theory, as well as geometric measure theory and of harmonic analysis, including the  theories of quasi-conformal mappings and of singular integrals. Some of these tools are used to study random point processes that arise in some models of fermions and in the spectral description of random matrices.

Members

Carme Cascante Canut

Konstantin Dyakonov

Jordi Marzo Sánchez

Xavier Massaneda Clares

Joaquim Ortega-Cerdà

Jordi Pau Plana

Our research focuses on theoretical aspects of Partial Differential equations (PDE) and related topics.

We study quite diverse problems, including: elliptic and parabolic PDE, Calculus of Variations, free boundary problems, nonlocal equations, geometric  inequalities, and relativistic quantum mechanics. Some of these lines of research have interesting connections to Geometry, Physics, or Probability.

Our group has received three ERC Grants as well as several awards, and you can find more information on our webpage: www.ub.edu/pde/

Members

Albert Clop Ponte

Gyula Csató

Xavier Ros Oton

Tomás Sanz Perela

The main research interests are in Algebraic Logic (logical systems like fuzzy, modal and intuitionistic logics, and metalogical problems with tools of universal algebra and category theory), Model Theory (definability issues in classical Mathematics, mainly in  the setting of Stability Theory and its generalizations), Proof Theory (proof systems and the computational and constructive content of proofs), Set Theory (large cardinals, combinatorics and forcing), foundations and in set-theoretic topology (cardinal  sequences for Boolean algebras and for Lindelöf P-spaces).

Membres

Joan Bagaria Pigrau

Enrique Casanovas Ruiz-Fornells

Joan Gispert Braso

Juan Carlos Martínez Alonso

Tommaso Moraschini

The Machine Learning and Artificial Intelligence at the University of Barcelona brings together a group of researchers interested in processing, analyzing, and interacting with intricate data systems, while also leveraging artificial intelligence methods to  derive insights and construct decision support systems. Their research covers theoretical foundations in machine learning, multi-agent systems, deep learning, and causal inference, as well as applied science across fields such as computer vision, natural  language processing, recommender systems, health and medicine, employing Artificial Intelligence techniques. Additionally, the group delves into methodological aspects, including the development of reliable and fair AI systems.

Members

Maite López Sánchez

Daniel Ortiz Martínez

Oriol Pujol Vila

Petia Radeva

Maria Salamó Llorente

Santi Seguí Mesquida

Nahuel Statuto

Jordi Vitrià Marca

In this interdisciplinary research line, researchers investigate innovative solutions at the intersection of Artificial Intelligence (AI) and diverse domains. This dynamic field encompasses AI’s transformative impact on healthcare and life sciences, leveraging advanced algorithms in medical image analysis, trustworthy medical AI, and personalised medicine. Social sciences, such as education or business management and administration, benefit from AI applications, contributing to cognitive science and enriching  the exploration of societal challenges. Robotics, too, witness the integration of AI, enhancing the autonomy and adaptability of intelligent systems. Anchored in Biomedical and Social Data Science, this research line navigates the complexities of large datasets,  exploring new pathways in understanding, diagnosis, and treatment. The goal is to forge intelligent, ethical and effective solutions, shaping a future in which AI is harmoniously intertwined with the complexities of life sciences, social dynamics and  technological advances.

Descriptors: AI for healthcare and life sciences, AI for social sciences, AI in education, AI in business management and administration, AI in robotics, cognitive science, medical image analysis, AI-powered personalized medicine, trustworthy medical AI,  Biomedical Data Science

Members

Simone Balocco

Ignasi Cos

Oliver Fernando Díaz Montesdeoca

Polyxeni Gkontra

Laura Igual Muñoz

Karim Lekadir

Eloi Puertas Prats

Computer Vision (CV) is a multidisciplinary field that enables computers to interpret and understand visual information from the world. It involves the development of Deep learning algorithms and systems that allow machines to gain high-level  understanding from digital images or videos. The goal of CV is to replicate and improve upon human vision capabilities. CV problems cover image processing, feature extraction, object recognition, object detection, image segmentation, scene understanding,  3D reconstruction, motion analysis, etc. Applications of CV include autonomous vehicles, medical imaging, surveillance, augmented reality, facial recognition and industrial automation, just to mention a few.

Computer Graphics (CG) is a field of study and technology that involves the creation, manipulation, and representation of visual images and animations using computers. CG encompasses a wide range of techniques and technologies for generating and processing visual information. Key components and concepts include rendering, modeling, animation, texturing, shading, computer-generated imagery, computer-aided design, virtual reality, graphics APIs, raster and vector graphics, GPU-based optimizations, etc. CG plays a crucial role in various applications, including entertainment, design, simulation, virtual reality, data and scientific visualization.

Human-Computer Interaction (HCI) is a field of study and research that focuses on the design and use of computer technology, particularly the interaction between humans and computers. The goal of HCI is to create user interfaces and systems that allow effective and satisfying interactions between users and computers. Key aspects of HCI include User-Centered Design, User Experience Design, Usability, Interaction Design, Information Architecture, Accessibility, Cognitive Psychology, Human Factors Engineering, User Research, Natural Language Interfaces, etc. HCI plays an essential role in ensuring that the design of human-computer interfaces keeps pace with user expectations and needs.

Members

Albert Clapés Sintes

Sergio Escalera Guerrero

Ricardo Marques

Ana Puig Puig

Petia Radeva

Mireia Isabel Ribera Turró

Inmaculada Cristina Rodríguez Santiago

Julio Cezar Silveira Jacques-Junior