GFMUL: Group of Mathematical Physics of the University of Lisbon

Project funded by Fundação para a Ciência e a Tecnologia, I.P. (FCT) (Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento B), grant UIDB/00208/2020. Funded amount: EUR 409,500, as stated by the source. Runs 2020-01-01 to 2024-12-31. Keywords: Stochastic Analysis, Geometric spectral theory and shape optimisation, Quantum Geometry and Pseudo differential operators, Topological gauge theories and quantum gravity. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2026-07-23); national funding data, not CORDIS; selected because its keywords name quantum. Abstract given by the source: 10.2 Summary in English for general dissemination purposes The Group of Mathematical Physics of the University of Lisbon (GFMUL) will push forward his programs of Stochastic Analysis, where the tools of Classical Mechanics are deformed to accommodate trajectories as irregular as Brownian ones.The whole point of this program is to preserve as much as possible the main geometric structures of the classical theory. We have an original method to do this which also applies, for instance, to Fluid Dynamics, allowing to treat dissipative systems such as the Navier-Stokes equation. Geometric Spectral theory, devoted to the relations between geometry of surfaces and spectrum of differential operators, will be another of GFMUL main research lines, as well as problems of Analysis and Geometry of pseudo differential operators relevant in Quantum Mechanics.Those tools are also quite useful in questions regarding Quantum foundations. An ambitious theoretical approach to Quantum graphs will be elaborated in our center. Quantum graphs are structures of vertices connected by edges, together with a (pseudo) differential Schroedinger operator acting on functions defined on individual edges. Geometric aspects of Quantum Theory in infinite dimension, i.e. of Quantum Field Theory, will remain one of our research topics, with emphasis on general notions of Integrability. Originated in Hamiltonian Mechanics, where Integrability means that the trajectories of the system are confined to submanifolds of the phase space and the solution of dynamical equations can be formulated by explicit integrals, it takes today different forms and relates with Algebraic Geometry, Random Matrix theory and other parts of mathematics. One aspect of this research project will be the study of the consequences of an important result found at GFMUL recently on the correspondence between Ordinary Differential equations and Integrable Models.This will involve understanding its connections with String Theory and [shortened; the full text is on the OpenAIRE page]

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Fundação para a Ciência e a Tecnologia, I.P. (FCT). Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The GFMUL project at the University of Lisbon, funded by FCT with EUR 409,500, runs from January 1, 2020, to December 31, 2024. It focuses on Stochastic Analysis and related fields, aiming to preserve geometric structures in classical theories. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.