Symposium on Clifford Algebras, Mathematical Physics and Related Topics

July 30, 2018, Federal University of ABC


Nelson José Rodrigues Faustino

Room: 518-2, Bloco A, Campus Santo André
Phone Number: +55 (11) 4996-8314















Aim of the symposium


The symposium is meant as an opportunity to join postgraduate students and researchers interested on Clifford algebras and mathematical physics. The different talks will shed some light on the broad variety of research topics in the interface between pure and applied mathematics.

During the symposium the participants will have the opportunity to exchange ideas, in a very informal style, with the lecturers. Successfully participants will receive a certificate of attendance.




If you are interested on attending the symposium, please send me an e-mail, including your complete name and host institution. There is no registration fee.


Lecturers and Participants


1.     Lívia Fernandes BARROS, Nuclear and Energy Research Institute (IPEN/USP), Brazil

2.     Robson Zacarelli DENKE, Regional University of Blumenau (FURB), Brazil

3.       Carlos Andrés Palechor IPIA, Federal University of ABC (UFABC), Brazil

4.       Nelson José Rodrigues FAUSTINO, Federal University of ABC (UFABC), Brazil

5.       Sergio Augusto Giardino FILHO, Federal University of Rio Grande do Sul (UFRGS), Brazil

6.     Malika Ait Ben HADDOU, Moulay Ismail University, Morocco

7.     El Hassan El KINANI, Moulay Ismail University, Morocco

8.     Paul Charles LEOPARDI, University of Melbourne & Australian Government, Bureau of Meteorology, Australia

9.       Aquerman Yanes MARTINHO, Federal University of ABC (UFABC), Brazil

10.   Zouhair MOUAYN, Sultan Moulay Silimane University, Morocco

11.   Pedro Lauridsen RIBEIRO, Federal University of ABC (UFABC), Brazil

12.   Roldão da ROCHA, Federal University of ABC (UFABC), Brazil

13.   Hector Leny Carrion SALAZAR, Federal University of Rio Grande do Norte (ECT/UFRN), Brazil



Timetable Schedule







Title and Abstract

Morning Session


Welcome Coffee

Opening Session




Zouhair Mouayn

(chair: Nelson Faustino)


Analysis of photon-count number distributions associated with higher Landau levels

By constructing generalized coherent states, to each Euclidean Landau level corresponds a generalized Poisson distribution and to each hyperbolic Landau level is attached a generalized negative binomial distribution.  For these probability distributions, we write atomic decompositions and we discuss the nonclassical nature of the associated coherent states. We derive Lévy-Khintchine-type representations of their characteristic functions  when the latters do not vanish and deduce that they are quasi-infinitely divisible except for lowest Landau levels​.​

By considering the total variation of the obtained quasi-Lévy measures, we introduce new infinitely divisible distributions.



Sergio Giardino

(chair: Nelson Faustino)


Quaternionic quantum mechanics in real Hilbert space

We will entertain a novel formulation of quantum mechanics where the wave functions are quaternionic and the Hilbert space is real. We will consider its physical motivations, mathematical consistency and exciting directions for future research.




Coffee Break




Paul Leopardi

(chair: Sérgio Giardino)


Gastineau-Hills' quasi-Clifford algebras and plug-in constructions for Hadamard matrices

Talk based on the preprint



 Malika Ait Ben Haddou

(chair: Sérgio Giardino)


·         Pseudo-Euclidean Alternative Algebras
Talk based on the paper




Lunch Break


Afternoon Session


El Hassan El Kinani (chair: Zouhair Mouayn)


Invariant Subspace Method: Application to Nonlinear Dispersive Equation with time-Caputo-Fabrizio Fractional Derivative

In this work, the invariant subspace method is applied to the nonlinear dissipative equation

with time fractional Caputo-Fabrizio derivative. The obtained reduced system of nonlinear ordinary

·         fractional equations is solved by using the Laplace transform method and with using of some useful properties of Mittag-Leffler function. Then, some exact solutions of the proposed time fractional nonlinear equation are found. 



Pedro Lauridsen Ribeiro (chair: Zouhair Mouayn)


Hyperbolic PDE systems, hyperbolic polynomials and generalized
Clifford algebras: an interdisciplinary panorama
Since D'Alembert's introduction of the wave equation for a
vibrating string, hyperbolic partial differential equations (PDE's)
has constituted a cornerstone of mathematical physics. This class of
PDE's is distinguished for being the only one within which the
noncharacteristic Cauchy problem is well posed in the smooth category
(Lax-Mizohata theorem), which demands on its turn that the (determinant
of) the principal symbol be a so-called hyperbolic polynomial in the
cotangent fiber variables: namely, a multivariable homogeneous
polynomial p is said to be hyperbolic along a certain direction y if
p(y) is not zero and for all x the one-variable polynomial that maps
t to p(x+ty) has only real roots. Hyperbolic polynomials have a rich
causal strucuture encoding the finite propagation speed of solutions
of the associated PDE's, which is generated by the cones of its
"hyperbolic vectors" y as above. Such vectors may be thought of as
"timelike", just like for a quadratic form of Lorentz signature ( =
principal symbol of the wave equation), which is the quintessential
example of a hyperbolic polynomial. The study of this class of
polynomials in its own right was started by Garding in the 50's aiming
back at PDE applications but later it grew well beyond such boundaries,
ranging from control theory to the recent striking proof of the Kadison-
Singer conjecture in operator algebras due to Marcus, Spielman and
Srivastava. A still unsolved conjecture in the study of hyperbolic
polynomials itself is the so-called generalized Lax conjecture,
which states that any cone of hyperbolic vectors with respect to some
hyperbolic polynomial is linearly isomorphic to the cone of positive
definite matrices of a certain rank. One of the strongest results
towards the solution of this conjecture has been recently put forward
by Netzer and Thom, who reformulated the latter in terms of a certain
generalized Clifford algebra associated to a given hyperbolic
polynomial. The goal of this talk is to present a broad survey of the
above developments, together with a few related results of my own
obtained in ongoing joint work with
Michael Forger (IME-USP).


15:35 – 16:00


Coffee Break




Nelson Faustino et al.

Round Table

Closing Session

Further topics of research


How to Reach the UFABC Campus?


         By Metro and Train

The UFABC Campus of Santo André is located across the Prefeito Celso Daniel/Santo André train station, Line 10 (Turquesa (pt-br)- Turquoise ) of the CPTM.

If you intend to come from São Paulo city by metro, you must take Line 2 (verde (pt-br) -green ) towards Vila Prudente. On the metro station of Tamanduateí you must exchange to CPTM to Line 10 towards Mauá/Rio Grande da Serra.



Symposium partially sponsored by