Cristina Serpa has a PhD in Mathematics (Mathematics Analysis), from the Faculty of
Sciences of the University of Lisbon. The topic of her thesis is Systems of Iterative
Functional Equations: Theory and Applications. Her background education includes a
strong mathematical basis, and studies in economics and management.
At present, she is an invited assistant professor at the Mathematics Department of
ISEL - Instituto Superior de Engenharia de Lisboa and her teaching duties recently
focus on curricular calculus units for engineering degrees. She has a vast teaching
experience in several courses, and Universities. She regularly is an advisor/co-advisor
for final projects/internships of undergraduate/graduate students.
Her professional path also includes the responsibilities of technical economics support
on regional and urbanism activities, for Regional Institutions and the City Hall of
Lisbon.
She is an integrated member at CMAFCIO - Centro de Matemática, Aplicações Fundamentais
e Investigação Operacional of the Universidade de Lisboa.
She collaborates with the SPM – Sociedade Portuguesa de Matemática, namely being a
member of the organization of an annual conference. She does regular review activities
for scientific journals and for Mathematical Reviews (MathScinet).
She makes research related to fractals, both at the fundamental theoretical level
and within its applications (such as physics, corporate studies, material science),
including fractal calculus (generalization of the classical calculus, defining the
differential and the integral in fractal domains, like Cantor sets).
She autonomously created the fractal regression method and developed a corresponding
software to obtain real data functions, which is being incorporated in recent research
papers.
She is able to do works with creativity, rigor, and deep theoretical results, as well
to stimulate young people, senior researchers and diverse teams to create science
(fundamental and applied areas, both multidisciplinary and internationally).
She has an extended network of international collaborators and is very active in scientific
activities (conferences with oral presentations, papers, book chapters, editorial
responsibilities, conference organization, poster presentation, and pedagogical material).
She is the head guest editor of the special issue "The Materials Structure and Fractal
Nature" of Fractal and Fractional, a first quartile journal.
Her key mathematical innovations in the literature are: the compatibility conditions
and the explicit representation of solutions of non-affine problems for systems of
iterative functional equations; and the definition, development and applicability
of the fractal regression method. The systems studied have solutions with fractal
structure and are those functions that are bases for fitting real data to Fractal
Regression Functions (FRF).
The FRF has numerous advantages regarding the Fractal Interpolation Functions (FIF),
namely, it identifies the fractal shape, regarding the self-similarity of the data,
and it allows to deeper analyse of various fractal levels of self-replication. FIF
is the method usually included in literature.
The possibilities of application of this method are wide, and the papers already published
are related to multidisciplinary scientific contexts and applied areas, such as nanomaterials,
physics, and corporate studies. Other areas in preparation to future works are financial
variables, and characterization of brain comparing health people, with injured from
accidents.
She aims to deeper its mathematical theoretical results in terms of 2D Fractal Regression,
to extend them to broader applications, and to stimulate an innovative educational
program for graduate students in universities.
For recommendations, please ask for senior researchers Peter Massopust (Technische
Universitat Munchen, Germany, massopust@ma.tum.de) and María A. Navascués (University
of Zaragoza, Spain, manavas@unizar.es).