Completed Projects and Programmes

Projects and programmes list

Applied Mathematics: from Dynamical Systems to Cryptography

Funded by Fundação para a Ciência e a Tecnologia & University of Texas at Austin.

Reference: UTAustin/MAT/0057/2008

09/01/2009 — 08/31/2013

Principal Investigator: Diogo Gomes

In this project we bring together researchers from several areas in Applied Mathematics including Dynamical Systems, Financial Mathematics, Game Theory, Optimal Control, Viscosity Solutions, Number Theory, and Cryptography. In all these areas there are strong research groups both in Portuguese Universities as well as in the University of Texas at Austin. The UTAustin|Portugal initiative presents a unique opportunity to foster scientific interactions between groups in Portugal and UT Austin.

Number of participants: 28.

Brazilian-European partnership in dynamical systems

Funded by Marie Curie Action IRSES — European Commission.

Reference: PIRSES-GA-2012-318999

01/01/2013 — 12/31/2016

Coordinator: Jeroen S. W. Lamb (Imperial College)

Coordinator at IST: Miguel Abreu

The project involves 21 European partners and 11 Brazilian partners.

Number of participants: 32.

Categorification, quantization and knots

Funded by Fundação para a Ciência e a Tecnologia.

Reference: FCT Investigator Program, Ref. IF/00998/2015

01/01/2017 — 12/31/2021

Principal investigator: Marko Stosic

The principal goal of this research project is to study the concepts of categorification and quantization, in particular in the context of quantum polynomial link invariants. The main line of this interdisciplinary proposal comes from surprising and exciting connections between the knot theory and homological knot invariants on the mathematical side, and quantum field theory and string theory on the physics side, with outcomes in other fields, like number theory or spectral curves.
 

CoLab Program — UT Austin | Portugal

Funded by Fundação para a Ciência e a Tecnologia.

01/01/2010 — 12/31/2017

The Center for Mathematical Analysis, Geometry, and Dynamical Systems is one of the participating research units in this cooperation program between Portuguese institutions and the University of Texas at Austin.

Contact and symplectic topology

Funded by Research Networking Programme — European Science Foundation.

Reference: CAST

01/27/2010 — 01/26/2015

Member of Steering Committee in Portugal: Sílvia Anjos

Other Members of the Steering Committee:

• Frédéric Bourgeois – Programme Chair
• Vincent Colin
• Kai Cieliebak
• András Stipsicz
• Michael Entov
• Paolo Lisca
• Robert Vandervorst
• Aleksy Tralle
• Francisco Presas
• Tobias Ekholm
• Felix Schlenk
• Ivan Smith

The goal of this network is to stimulate exchange between researchers from all branches of contact and symplectic topology, in order to create a comprehensive perspective on the field and make progress on some of the basic open questions. The European scale of the network reflects the global nature of these questions as well as the European strength in the subject. The planned activities include workshops, research collaborations, and the exchange of PhD students and postdocs.

The research themes of CAST include:

• Fukaya categories and mirror symmetry,
• Floer homology and Hamiltonian dynamics,
• Symplectic field theory,
• Contact Topology,
• Complex geometry and Stein manifolds,
• Topology of symplectic manifolds,
• Groups of symplectomorphisms and contactomorphisms.

Degenerate elliptic and parabolic equations and its applications to front propagation

Funded by Fundação para a Ciência e a Tecnologia.

Reference: UTA_CMU/MAT/0007/2009

08/10/2011 — 08/09/2014

Principal investigator: Diogo Gomes

The main goals of the project are the study of PDEs arising in front propagation, namely degenerate elliptic and parabolic equations, their application to concrete problems such as ocean fronts, and the development of numerical tools for the analysis of inverse problems in front propagation. We foresee that the developed techniques will be of interest for other problems also, such as mathematical finance, non-linear filtering, classical mechanics (Aubry-Mather theory and its extensions), mathematical biology, mean field games, homogenization and stochastic PDEs.

Number of participants: 16.

Geometrical and Algebraic Structures on the Space of Quantum Theories

Funded by Fundação para a Ciência e a Tecnologia.

Reference: FCT 02/SAICT/2017/28784

10/01/2018 — 09/30/2021

Principal investigator: Ricardo Schiappa

This project addresses mathematical structures in the space of all possible quantum theories. The space of all QFTs is infinite-dimensional, with CFT fixed-points linked by paths corresponding to RG flows. These CFTs are the building blocks of all possible quantum theories (including theories of quantum gravity and black holes). Our goal is to understand the space of all theories by first understanding some special subsets. We use complementary approaches, such as Resurgent Analysis, Bootstrap Techniques, and Localisation. These approaches solve quantum theories described by random matrix models, CFTs in diverse dimensions, and quantum theories with localisable observables. The very same theory may be approachable using these different techniques, leading to complementary information. By solving different special sets of quantum theories, we expect to describe geometrical and algebraic structures on local patches of the full space of quantum theories.
 

Geometry and Mathematical Physics

Funded by Fundação para a Ciência e a Tecnologia.

Reference: EXCL/MAT-GEO/0222/2012

05/01/2013 — 04/30/2016

Principal investigator: Miguel Abreu

The project aims at fostering the interaction of research in Geometry and Mathematical Physics within the Department of Mathematics of IST and throughout the country, through the stimuli for interaction among researchers, the reinforcement of international connections, the attraction of post-docs and doctoral students, and the organization of seminars, short courses and international meetings.

Number of participants: 39.

Geometry of quantization

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT/119689/2010

01/01/2012 — 12/31/2014

Principal investigator: José Mourão

Study of the dependence of quantization on the choice of polarization, in the new formalism provided by the distributional approach to the prequantum bundle over families of complex structures. In this formalism, it is possible to include real and mixed nonnegative polarizations as points in the boundary of the space of complex structures.

Number of participants: 11.

Global properties of solutions of the Einstein equations

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT-ANA/1275/2014

01/01/2016 — 06/30/2020

Principal Investigator: João Lopes Costa

The main goal of the project is the study of global properties of solutions of the Einstein equations, especially in what concerns cosmic censorship and the formation of singularities in general relativity. This requires the use of techniques of geometry and analysis, particularly hyperbolic partial differential equations.
 

Number of participants: 13.

Hamiltonian Actions and Integrability in Geometry and Topology

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT/117762/2010

03/01/2012 — 02/28/2015

Principal investigator: Miguel Abreu

Devoted to certain global aspects of symplectic, contact and Poisson geometries, where Hamiltonian actions and integrability questions are relevant. These aspects include: Kähler metrics invariant inder Hamiltonian group actions; topology of certain Hamiltonian diffeomorphism groups; noncommutative integrable systems; polygon spaces and moduli spaces of bordered Riemann surfaces; Lagrangian intersection problems; Hamiltonian diffeomorphism groups of Poisson manifolds; complex hypersurfaces.

Number of participants: 17.

Higgs bundles and character varieties

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT/120411/2010

03/01/2012 — 02/28/2015

Principal investigator: Carlos Florentino

This project deals with the geometry and topology of two classes of intimately related spaces: on one side, we have the moduli spaces of Higgs bundles or other holomorphic objects over a complex manifold, and on the other side we have character varieties, which are moduli spaces of representations of a finitely generated group into a Lie group.

In this project, we plan to address some of the facets of this profitable connection that are still undeveloped. Our approach will be a natural continuation of many important established results that were obtained in recent years by many mathematicians, including results from members of the project.

Number of participants: 6.

Higher Structures and Applications

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT-PUR/31089/2017

07/01/2018 — 06/30/2021

Principal investigator: Roger Picken

This project uses higher algebraic structures to obtain new results in topology, geometry and algebra, and to develop applications in related areas of physics and in topological quantum computation.
 

Number of participants: 8.

Hydrodynamic Limits and Equilibrium Fluctuations: universality from stochastic systems

Funded by European Research Council - Starting Grant.

Reference: 715734

12/01/2016 — 11/30/2021

Principal investigator: Patrícia Gonçalves

The research project aims at characterizing the universality of the macroscopic behavior of some physical systems from underlying microscopic stochastic dynamics, by deriving the macroscopic laws, namely, (stochastic) partial differential equations, which govern the space-time evolution of the thermodynamic quantities of those physical systems.
 

Number of participants: 8.

Modeling and Analysis of Coastal Hydrodynamics and Erosion

Funded by Fundação para a Ciência e a Tecnologia.

Reference: UTAP-EXPL/MAT/0017/2017

11/01/2018 — 10/31/2020

Principal investigator: Juha Videman

Coastal ocean regions around the world are threatened by a variety of factors and the increasing risk and associated impacts have catalysed efforts to increase our understanding of the coastal ocean environment and our ability to make quantitative predictions of coastal hydrodynamics. In this project, we propose to build a numerical code based on hybridised discontinuous finite element methods for studying coastal hydrodynamics and sediment erosion with specific emphasis on regions of the Texas-U.S. and Portuguese coasts. Our goal is to develop, analyse and implement high-order finite element methods on unstructured meshes which include appropriate wave physics at various wave-lengths and wave numbers. This allows for capturing multi-scale wave physics from deep ocean basins to the continental shelf to complex coastal systems including barrier islands, inlet, bays, and estuaries.

Number of participants: 3.

Non-linear degenerate elliptic equations and systems

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT/114397/2009

01/01/2011 — 12/31/2013

Principal investigator: Diogo Gomes

This project focus on equations and systems of non-linear possibly degenerate elliptic partial differential equations, as well as its applications to stochastic optimal control, mean field games and Aubry-Mather theory.

Number of participants: 14.

Portuguese Algebraic Geometry Community

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT-GEO/0675/2012

01/25/2013 — 01/24/2015

Principal investigator: Margarida Mendes Lopes

This project aims to promote the interaction between algebraic geometers in Portugal and is focused on problems linked to moduli spaces and classification of objects of algebraic geometry.

Number of participants: 15.

Quantization and Kahler Geometry

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT-GEO/3319/2014

04/01/2016 — 06/30/2020

Principal investigator: João Pimentel Nunes

The project studies the relations between Kahler geometry and geometric quantization. The focus is on degenerating families of Kahler metrics, in the space of Kahler metrics for a fixed cohomology class equipped with the Mabuchi metric, and relations to both Kahler and real polarizations in quantization.
 

Number of participants: 7.

Representations of Operator Algebras and Applications

Funded by Fundação para a Ciência e a Tecnologia & CNRST - MOROCCO.

Reference: Po 441.00 CNRST - MOROCCO

05/25/2013 — 05/24/2015

Principal investigator: Paulo Pinto

This project aims to promote the bilateral cooperation between researchers in Portugal and Morocco and is focused on problems linked to operator algebras and their relations with dynamical systems and mathematical physics.

Number of participants: 7.

Research Chair in String Theory

Funded by Fundação para a Ciência e a Tecnologia & Instituto Superior Técnico.

10/01/2009 — 09/30/2014

Gabriel Lopes Cardoso holds the Invited Research Chair on Mathematical Physics and String Theory. The main research goals are in the area of String Theory, with very strong links to Mathematical Physics, Geometry and Topology. This is a most promising venue for future research, lying at the interface between Mathematics and Theoretical Physics, and with proven major contributions to both fields.

Stability of nonautonomous dynamical systems

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT/117106/2010

03/01/2012 — 02/28/2015

Principal investigator: Claudia Valls

The main objective of the project is to pursue several directions of research in dynamical systems and differential equations, with emphasis on the study of stability of nonautonomous dynamics, particularly in the presence of nonuniform hyperbolicity, and on the qualitative study of polynomial vector fields and equations of mathematical physics, including their integrability.

Number of participants: 3.

Symplectic Geometry and Conservative Dynamics

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT-PUR/29447/2017

10/01/2018 — 09/30/2021

Principal investigator: Miguel Abreu

This project brings together experts in different aspects of the area of Symplectic Geometry and its applications, and aims at building bridges between different techniques, creating novel enhancements and stimulating new developments in the field. The area of application of Symplectic Geometry that better represents the unifying theme of this project is Conservative Dynamics, considered in a broader context, focusing on its links with symplectic and contact topology, toric actions, Seidel’s morphism and Gromov-Witten theory, Poisson geometry and integrable systems.
 

Number of participants: 5.

Toeplitz Operators and Riemann-Hilbert problems: at the crossroad of operator theory and complex analysis

Funded by Fundação para a Ciência e a Tecnologia.

Reference: PTDC/MAT/121837/2010

02/01/2012 — 01/31/2015

Principal investigator: Maria Cristina Câmara

The central object of this project is the interplay between Toeplitz operators and Riemann-Hilbert problems. It aims to study various properties of Toeplitz operators and to develop new methods to solve Riemann-Hilbert problems that arise in many areas in mathematics, as well as in connection with a variety of problems in Physics and Engineering, showing that progress in one topic goes hand in hand with progress in the other.

Number of participants: 3.