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Activity Funded

Group of Mathematical Physics

Grupo de Física Matemática

Reference
UID/00208/2025
Project Start Date
2025-01-01
Project End Date
2029-12-31
Principal Investigator
Funding Program
Avaliação UID 2023/2024

Abstract

The Group of Mathematical Physics (GFM), https://fisica-matematica.pt/en/, has recently moved from FCUL to IST. At IST we have already multiple collaborations, that will be strengthened. We will push forward our research programs in the following areas: Integrable Systems and Geometry: they are fundamental components of Math. Physics. The area has played a pivotal role in modern mathematics and its applications across various scientific disciplines, as the study of dynamical systems with special symmetries and geometric structures offers insights into more general dynamical systems. Spectral Theory of Differential Operators: it is a classical topic in Math. Physics. We study qualitative and quantitative properties of operators such as Laplacians and Schrödinger operators, in contexts like Euclidean domains, Riemannian manifolds and quantum graphs. The analysis is complemented by developing new methods for the study of shape optimisation problems in spectral theory, with applications in classical and new problems coming from physical applications such as musical acoustics, civil and mechanical engineering. Stochastic Analysis and Optimal Transport: Stoch. analysis is the analytical study of random phenomena. We focus on topics like Feynman integral, Stoch. deformation, Stochastic Geometric Mechanics, Stoch. optimal control and SPDEs. The so-called “Schrödinger problem”, originally a variational principle, can be regarded as problem of entropy minimisation converging toward Benamou-Brenier fluid mechanical interpretation of deterministic optimal transport. This provides deep insights into fundamental questions such as curvature, geometry, functional inequalities, etc. Quantum Mechanics and Quantum Gravity: we study quantum gravity using a path-integral approach where the smooth-manifold spacetime is replaced with a piecewise linear manifold, representing a triangulation of the manifold. We are also interested in Higher Gauge Theory and in Standard quantum mechanics. We workmainly in the context of the phase space formulation of quantum mechanics, addressing longstanding problems whose solutions are important for applications in quantum information and quantum computing. We will reinforce our international network of collaborators, apply to national/international projects and grants and continue our tradition of organisation of conferences and meetings. We will maintain our 3 series of seminars, in collaboration with colleagues of CAMGSD (cf. GFM’s webpage) and will launch another one soon. Advanced training is one of our priorities, PhD thesis advising, also Master and Bachelor mentoring. We intend to continue receiving international early stage researcher. Another priority is to invest in the recently launched FCT-Tenure program and to be able to integrate researchers into permanent career positions. We have been increasing the number of outreach activities of the centre; we intend to participate but also organise some of these activities.

Institutions

Main Institutions

  • Universidade de Lisboa Grupo de Física Matemática (ULisboa GFM)
  • Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento (IST-ID)

Funding 935.888,38 €

Fundação para a Ciência e a Tecnologia (FCT) - Portugal

935.888,38 €