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António Machiavelo
António Machiavelo
University of Porto
Portugal
Daniele Corradetti
Daniele Corradetti
University of Algarve
Portugal
Federico Thomas
Federico Thomas
Institut de Robotica i Informàtica Industrial
Spain
Kamal Diki
Ghent University
Belgium
Abstracts
Abstracts
António Machiavelo
António Machiavelo
University of Porto
Portugal
Title of the talk: Arithmetic in the Quaternions and Diophantine Problems
Abstract: In this talk we will describe what is known about the arithmetic in the ring of Hurwitz integers, a very special subring of the quaternions, and the use of this arithmetic in solving some Diophantine problems, i.e. problems where one seeks integer solutions of some polynomial equations or systems of polynomials equations, as well as some open problems in this context.
Short Bio, including current research interests
I have a PhD from Cornell University, USA, with a thesis in Algebraic Number Theory. I am Assistant Professor of the University of Porto, and member of the Center of Mathematics of the University of Porto. My mathematical research interests are in Number Theory — recently focused on quaternion arithmetic and its use to solve Diophantine problems —, Analytic Combinatorics applied to Theoretical Computer Science, and I also have an interest in the History and Philosophy of Mathematics.
Daniele Corradetti
Daniele Corradetti
University of Algarve
Portugal
Title of the talk: 8-Dimensional Composition Algebras and Real Forms of Exceptional Lie Groups G2, F4, and E6
Abstract: The generalised Hurwitz theorem states that exist only fifteen composition algebras over any given field: seven Hurwitz algebras (four division and three split), six para-Hurwitz algebras (three division and three split) and two Okubo algebras (one division and one split). Of these fifteen algebras only three are division composition algebras of dimension eight: the Octonions, which are unital; the para-Octonions that are para-unital and the Okubo algebra which is non-unital. In this talk we will show how all of them are suitable for the construction of the 16-dimensional Moufang plane and how the collineation groups of such a plane allows the realisation of all possible real forms of the Lie Groups G2 and F4 along with two real forms of E6.
This work is in collaboration with Alessio Marrani and Francesco Zucconi.
Short Bio, including current research interests
Member of Grupo de Física Matemática (IST) received his master degree in mathematics from Università degli Studi di Pisa and just completed his PhD in Mathematics with the University of Algarve. His research interests include non-associative algebras, composition algebras, exceptional Lie groups and Jordan algebras along with their generalisations. A special interest is on Octonionic and Okubo algebras on which he has already published numerous articles.
Federico Thomas
Federico Thomas
Institut de Robotica i Informàtica Industrial
Spain
Title of the talk: Approximating Dual Quaternions by Double Quaternions with Applications
Abstract: While the real matrix representations of quaternions and double quaternions directly follow from the analysis of rotations in 4-dimensional Euclidian space, this kind of representations for dual quaternions and octonions require the introduction of some approximations. In this presentation we analyze all these representations and consider their various applications in physics.
Short Bio, including current research interests
Prof. Federico Thomas received the telecommunications engineering degree in 1984, and the Ph.D. degree in computer science in 1988, both from the Technical University of Catalonia (UPC).
In 1991, he obtained a NATO postdoctoral fellowship at the University of Massachusetts. In 1999, He was visiting professor at the Oxford University Computing Laboratory. He was also invited professor at the École Central de Nantes (France) and the University of Ferrara (Italy).
He served as an associated editor of IEEE Transactions on Robotics, ASME Journal of Mechanisms and Robotics, and The International Journal of Mechanics and Control.
His current position is Professor of Research of the Spanish National Research Council (CSIC) at the Instituto de Robótica e Informática Industrial, in Barcelona, where he served as a former director.
His research interests include Distance Geometry and Clifford Algebras, and their application to Geometry and Kinematics.
Kamal Diki
Ghent University
Belgium
Title of the talk: An approach to quaternionic reproducing kernel Hilbert spaces via Clifford-Appell polynomials
Abstract: We use the classical Fueter mapping theorem to build a system of Clifford-Appell polynomials in the quaternionic setting. We will discuss various properties of such polynomials and study their algebraic behavior with respect to the well-known Cauchy-Kowalevski product. Then, based on this system, we study a family of quaternionic reproducing kernel Hilbert spaces in this framework. As particular examples, we will treat results in the case of Hardy and Fock spaces and present counterparts of creation, annihilation, shift, and backward shift operators. We will present some connections and applications of this approach to quaternionic polyanalytic functions and Schur analysis. If time allows, we will discuss extensions of these results in the Clifford case.
Short Bio, including current research interests
Dr. Diki is a mathematician from Morocco who obtained a Ph.D. in Mathematical Models and Methods in Engineering from Politecnico di Milano as a Marie Sklodowska-Curie fellow. He is interested in research topics involving (hyper)-complex analysis, reproducing kernel Hilbert spaces, operator theory, integral transforms, mathematics for quantum mechanics and time-frequency analysis, and kernel methods.
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