Linear, Algebraic and Combinatorial Structures.

The Group conducts research primarily on Representations of Groups, Matrix Theory and Linear Systems. It also pursues ongoing research on related topics: Hom-configurations, Sequence Subgroups in Finite fields, Rees Algebras of Modules, Symmetry of Tensors and Related Combinatorics, Cellular Automata and Non-Linear Dynamical Systems, Polytopes and Polygon Spaces, Riordan Matrices and Symbolic Calculus.

Representation of Groups

We use methods of Algebraic, Geometric and Combinatorial Representation Theory to study Character and Supercharacter Theories of Finite and Infinite (Topological) Groups. On the other hand, methods from Functional Analysis, Ergodic Theory and Topological Dynamics are used to study extreme characters and supercharacters of infinite groups which occur as inductive limits of finite groups. We also study the structure of Hopf algebra on the space of superclass functions defined on all finite unitriangular groups which is isomorphic to the combinatorial Hopf algebra of symmetric functions on noncommuting indeterminates, and explore applications in Algebra, Number Theory, Statistics and Algebraic Combinatorics.

Matrix Equations and Matrix Completion Problems

We study the existence of solutions of matrix equations and systems of matrix equations with some prescribed properties, and consider generalizations in order to study the stabilization of linear systems with input variables.

We also consider the existence of certain matrices with prescribed entries and properties, extend our research to operators in spaces of infinite dimension and to matrices over noncommutative rings, and consider engineering applications. We also study how the properties of a matrix vary under perturbations on some of its entries.

Matrix pencil completion problems

We search for an explicit and constructive solution for the general matrix pencil completion problem: describe the possible Kronecker invariants of a pencil with a prescribed subpencil. A related problem is to study small perturbations on pencils. We also explore purely combinatorial aspects of matrix completion problems, study the close relationship between completion problems of matrix pencils and the representation theory of quivers, and consider matrix problems arising from engineering areas, as computer vision and signal processing.

Symmetries of Tensors

Symmetries of tensors arise naturally in connection to the irreducible characters of the symmetric group. Schur-Weyl dualities provide a fruitful approach to the study of classical problems in different situations, namely in the study of symmetries of harmonic tensors, or in the setting of the infinite symmetric group. A related problem concerns about generalized matrix functions and their directional derivatives, and opens new lines of research.

Calabi-Yau triangulated categories

These appear in many branches of mathematics and physics: conformal field theory and string theory in theoretical physics, homological mirror symmetry in algebraic and symplectic geometry, and cluster-tilting theory in representation theory. Particular research is devoted to finding appropriate representation-theoretic categories associated to Riemann surfaces.

Sequence Subgroups in Finite fields

We describe of the non-standard configurations of f-sequence subgroups when f(t) is any polynomial.

Rees Algebras of Modules

We study several asymptotic and arithmetical properties of certain classes of modules arising in connection with Algebraic Geometry, such as equimultiple modules.

Cellular Automata and Non-Linear Dynamical Systems

We use timewise updating and spacewise updating to simulate complex systems with cellular automata, and derive certain exact analytical formulae to quantify the algorithmic complexity of spacewise evolution of certain cellular automata.

Combinatorial Game Theory

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News

IWOTA 2019

Published Jan 30, 2019 in FA LACS

The 30th International Workshop on Operator Theory and its Applications, IWOTA 2019 will be held from Monday July 22nd through Friday July 26th, at Instituto Superior Técnico, University of Lisbon, Portugal. IWOTA 2019 will be focused on the latest developments in Functional Analysis, Operator Theory and related fields. IWOTA 2019 intends to bring together mathematicians and engineers […]

CEAFEL Seminar

Published Dec 03, 2018 in LACS

On Friday, 07/12/2018, 15:45 — 16:45 — Room 6.2.33, Faculdade de Ciências da Universidade de Lisboa will take place a seminar by Jocelyn Lochon, Universidade de Lisboa with title “The asymptotic behaviour of the Super-Plancherel measure”.

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Members

Members

Ana L. Branco Correia

Academia Militar

Ana Margarida Neto

ISEG - U. Lisboa

Ângela Mestre

Bolseira FCT

Carlos A. M. André

Faculdade de Ciências, ULisboa

Carlos Pereira dos Santos

Faculdade de Ciências, ULisboa

Fernando C. Silva

Faculdade de Ciências, ULisboa

José Agapito Ruiz

Bolseiro FCT

Laura Azevedo

ISEL

Maria Amélia Fonseca

Faculdade de Ciências, ULisboa

Maria Antónia Duffner

Faculdade de Ciências, ULisboa

Maria da Purificação Coelho

Faculdade de Ciências, ULisboa

Maria Manuel Torres

Faculdade de Ciências, ULisboa

Marija Dodig

Investigadora FCT, ULisboa

Owen J. Brison

Faculdade de Ciências, ULisboa

Raquel Simões

Bolseira FCT

Sonia Carvalho

Susana Furtado

Faculdade de Economia, U. Porto

Collaborators

Filipe Gomes

PhD Student, FCUL (LisMath)

Inês Legatheaux Martins

PhD Student, FCUL

João Dias

PhD Student, FCUL (LisMath)

Jocelyn Lochon

PhD Student, FCUL (LisMath)

Maria da Graça Pereira

PhD Student, FCUL

Pedro J. Freitas

Faculdade de Ciências, ULisboa

Pedro Matos

PhD Student, FCUL (LisMath)

Tânia Zaragoza Silva

PhD Student, FCUL (LisMath)