{"id":313,"date":"2016-06-23T11:10:19","date_gmt":"2016-06-23T09:10:19","guid":{"rendered":"https:\/\/mat.ub.edu\/?page_id=313"},"modified":"2025-11-06T09:29:16","modified_gmt":"2025-11-06T08:29:16","slug":"recerca","status":"publish","type":"page","link":"https:\/\/mat.ub.edu\/en\/recerca\/","title":{"rendered":"Research"},"content":{"rendered":"

[vc_row][vc_column][vc_column_text]<\/p>\n

Research Lines<\/strong><\/span><\/p>\n

[\/vc_column_text][vc_tta_accordion c_align=”right” c_icon=”chevron” active_section=”666″ no_fill=”true” collapsible_all=”true”][vc_tta_section title=”Commutative Algebra and Algebraic Geometry” tab_id=”1708343294622-8bff626a-c830″][vc_column_text css=””]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,\u00a0 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\u00a0 theory and effective methods applied to Algebraic Geometry.<\/p>\n

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\u00a0 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.<\/p>\n

Members<\/strong><\/p>\n

Laura Costa Farr\u00e0s<\/a><\/p>\n

Carlos D\u2019Andrea<\/a><\/p>\n

Joan Elias Garcia<\/a><\/p>\n

Ricardo Garc\u00eda L\u00f3pez<\/a><\/p>\n

Mart\u00ed Lahoz Vilalta<\/a><\/p>\n

Simone Marchesi<\/a><\/p>\n

Rosa M. Mir\u00f3-Roig<\/a><\/p>\n

Joan Carles Naranjo del Val<\/a><\/p>\n

Andr\u00e9s Rojas Gonz\u00e1lez<\/a><\/p>\n

Mart\u00edn Sombra<\/a><\/p>\n

Santiago Zarzuela Armengou<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Number Theory” tab_id=”1708344383350-fc4e9278-3241″][vc_column_text]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\u00a0 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\u00a0 Program, there is interest on the Sato-Tate conjecture, Differential Galois Theory, diophantine equations and cryptography.<\/p>\n

Members<\/strong><\/p>\n

Paloma Bengochea<\/p>\n

Francesc Fit\u00e9<\/a><\/p>\n

Lu\u00eds V\u00edctor Dieulefait<\/a><\/p>\n

Xavier Guitart Morales<\/a><\/p>\n

Artur Travesa Grau<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Differential Geometry and Topology” tab_id=”1708344621902-b7434285-f778″][vc_column_text css=””]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\u00a0 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\u00a0 spaces, such as K\u00e4hler 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\u00a0 innovative and powerful technique for applications of Topology to Neural Networks and Data Science. More information at the Topology website.<\/a><\/p>\n

Members<\/strong><\/p>\n

Robert Cardona<\/a><\/p>\n

Carles Casacuberta Verg\u00e9s<\/a><\/p>\n

Joana Cirici<\/a><\/p>\n

Javier J. Guti\u00e9rrez Mar\u00edn<\/a><\/p>\n

Ignasi Mundet i Riera<\/a><\/p>\n

Leopold Zoller[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Combinatorics” tab_id=”1708344625123-0820061d-9afc”][vc_column_text css=””]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\u00a0 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\u00a0 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\u00a0 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\u00a0 (Cayley graphs, reflection arrangements, cluster algebras). More info at our website: https:\/\/www.ub.edu\/comb\/<\/a><\/p>\n

Members<\/strong><\/p>\n

Alberto Espuny<\/a><\/p>\n

Kolja Knauer<\/a><\/p>\n

Arnau Padrol Sureda<\/a><\/p>\n

Vincent Pilaud<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Stochastic Analysis” tab_id=”1708344856241-5685a9cc-17be”][vc_column_text]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\u00a0 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\u00a0 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\u00a0 the professional destination of doctoral students trained in this area.<\/p>\n

Members<\/strong><\/p>\n

Jos\u00e9 Manuel Corcuera Valverde<\/a><\/p>\n

David M\u00e1rquez Carreras<\/a><\/p>\n

Carles Rovira Escofet<\/a><\/p>\n

Marta Sanz-Sol\u00e9<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Dynamical Systems” tab_id=”1708344972676-880b373f-21d9″][vc_column_text css=””]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\u00a0 the systems fall in this study.<\/p>\n

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

More information at the Dynamical Systems webpage: https:\/\/www.ub.edu\/dynsys<\/a><\/p>\n

Membres<\/strong><\/p>\n

Kostiantyn Drach<\/a><\/p>\n

N\u00faria Fagella Rabionet<\/a><\/p>\n

Ernest Fontich Juli\u00e0<\/a><\/p>\n

Gerard G\u00f3mez Muntan\u00e9<\/a><\/p>\n

Marina Gonchenko<\/a><\/p>\n

Marcel Gu\u00e0rdia<\/a><\/p>\n

\u00c0lex Haro<\/a><\/p>\n

Xavier Jarque i Ribera<\/a><\/p>\n

\u00c0ngel Jorba Monte<\/a><\/p>\n

Leticia Pardo-Sim\u00f3n<\/a><\/p>\n

Joan Carles Tatjer Monta\u00f1a<\/p>\n

Arturo Vieiro Yanes<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Mathematical Analysis” tab_id=”1708345176625-250baf63-c62d”][vc_column_text css=””]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\u00a0 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.<\/p>\n

Members<\/strong><\/p>\n

Carme Cascante Canut<\/a><\/p>\n

Konstantin Dyakonov<\/a><\/p>\n

Matteo Levi<\/a><\/p>\n

Jordi Marzo S\u00e1nchez<\/a><\/p>\n

Xavier Massaneda Clares<\/a><\/p>\n

Joaquim Ortega-Cerd\u00e0<\/a><\/p>\n

Jordi Pau Plana<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Partial Differential Equations” tab_id=”1708345330546-c5723de0-8930″][vc_column_text css=””]Our research focuses on theoretical aspects of Partial Differential equations (PDE) and related topics.<\/p>\n

We study quite diverse problems, including: elliptic and parabolic PDE, Calculus of Variations, free boundary problems, nonlocal equations, geometric\u00a0 inequalities, and relativistic quantum mechanics. Some of these lines of research have interesting connections to Geometry, Physics, or Probability.<\/p>\n

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\/<\/a><\/p>\n

Members<\/strong><\/p>\n

Albert Clop Ponte<\/p>\n

Gyula Csat\u00f3<\/a><\/p>\n

Xavier Ros Oton<\/a><\/p>\n

Dom\u00e8nec Ruiz i Balet<\/a><\/p>\n

Tom\u00e1s Sanz Perela<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Mathematical Logic” tab_id=”1708345377087-19b25502-57b8″][vc_column_text css=””]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\u00a0 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\u00a0 sequences for Boolean algebras and for Lindel\u00f6f P-spaces).<\/p>\n

Membres<\/strong><\/p>\n

Joan Bagaria Pigrau<\/a><\/p>\n

Enrique Casanovas Ruiz-Fornells<\/a><\/p>\n

Joan Gispert Braso<\/p>\n

Juan Carlos Mart\u00ednez Alonso<\/a><\/p>\n

Tommaso Moraschini<\/a><\/p>\n

Alejandro Poveda<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Machine Learning and Artificial Intelligence” tab_id=”1708345459566-96fc9c0e-241d”][vc_column_text css=””]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\u00a0 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\u00a0 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.<\/p>\n

More information on the SGR website “Artificial Intelligence and Biomedical Applications”<\/a>.<\/p>\n

Members<\/strong><\/p>\n

Maite L\u00f3pez S\u00e1nchez<\/a><\/p>\n

Daniel Ortiz Mart\u00ednez<\/p>\n

Oriol Pujol Vila<\/a><\/p>\n

Petia Radeva<\/a><\/p>\n

Maria Salam\u00f3 Llorente<\/a><\/p>\n

Santi Segu\u00ed Mesquida<\/a><\/p>\n

Muriel Rovira<\/p>\n

Nahuel Statuto<\/p>\n

Jordi Vitri\u00e0 Marca<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Artificial Intelligence for Life Sciences and AI Applications” tab_id=”1708345524529-5f94a974-0dc7″][vc_column_text css=””]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\u00a0 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,\u00a0 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\u00a0 technological advances.<\/p>\n

More information on the SGR website “Artificial Intelligence and Biomedical Applications”<\/a>.<\/p>\n

Descriptors:<\/strong> 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,\u00a0 Biomedical Data Science<\/p>\n

Members<\/strong><\/p>\n

Simone Balocco<\/a><\/p>\n

Ignasi Cos<\/a><\/p>\n

Oliver Fernando D\u00edaz Montesdeoca<\/a><\/p>\n

Polyxeni Gkontra<\/p>\n

Laura Igual Mu\u00f1oz<\/a><\/p>\n

Karim Lekadir<\/a><\/p>\n

Eloi Puertas Prats<\/a>[\/vc_column_text][\/vc_tta_section][vc_tta_section title=”Computer Vision, Computer Graphics and Human-Computer Interaction” tab_id=”1708345610331-6afaaf2c-d160″][vc_column_text css=””]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\u00a0 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,\u00a0 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.<\/p>\n

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.<\/p>\n

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.<\/p>\n

More information on the SGR website “Artificial Intelligence and Biomedical Applications”<\/a>.<\/p>\n

Members<\/strong><\/p>\n

Xavier Bar\u00f3<\/p>\n

Albert Clap\u00e9s Sintes<\/p>\n

Sergio Escalera Guerrero<\/a><\/p>\n

Anna Puig Puig<\/a><\/p>\n

Petia Radeva<\/a><\/p>\n

Mireia Isabel Ribera Turr\u00f3<\/a><\/p>\n

Inmaculada Cristina Rodr\u00edguez Santiago<\/a><\/p>\n

Julio Cezar Silveira Jacques-Junior<\/a>[\/vc_column_text][\/vc_tta_section][\/vc_tta_accordion][\/vc_column][\/vc_row]<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

[vc_row][vc_column][vc_column_text] Research Lines [\/vc_column_text][vc_tta_accordion c_align=”right” c_icon=”chevron” active_section=”666″ no_fill=”true” collapsible_all=”true”][vc_tta_section title=”Commutative Algebra and Algebraic Geometry” tab_id=”1708343294622-8bff626a-c830″][vc_column_text css=””]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,\u00a0 moduli spaces […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-segell.php","meta":{"footnotes":""},"class_list":["post-313","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/pages\/313","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/comments?post=313"}],"version-history":[{"count":18,"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/pages\/313\/revisions"}],"predecessor-version":[{"id":2793,"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/pages\/313\/revisions\/2793"}],"wp:attachment":[{"href":"https:\/\/mat.ub.edu\/en\/wp-json\/wp\/v2\/media?parent=313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}