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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).
Identificação

Identificação pessoal

Nome completo
Maria Cristina Gonçalves Silveira de Serpa

Nomes de citação

  • Serpa, Cristina

Identificadores de autor

Ciência ID
1B15-DA44-023A
ORCID iD
0000-0002-8561-118X

Websites

Domínios de atuação

  • Ciências Exatas - Matemática

Idiomas

Idioma Conversação Leitura Escrita Compreensão Peer-review
Português (Idioma materno)
Inglês Utilizador proficiente (C1) Utilizador proficiente (C2) Utilizador proficiente (C1) Utilizador proficiente (C2) Utilizador proficiente (C2)
Francês Utilizador independente (B1) Utilizador independente (B2) Utilizador independente (B1) Utilizador proficiente (C1) Utilizador proficiente (C1)
Espanhol; Castelhano Utilizador independente (B2) Utilizador proficiente (C2) Utilizador independente (B1) Utilizador proficiente (C2) Utilizador proficiente (C2)