Marcio Gomes

Residency Period: 08/01/2011 to 07/31/2012

Marcio Gomes holds a Bachelor’s degree in Mathematics from the Federal University of Minas Gerais (1975), a Master’s degree in Mathematics from the Federal University of Minas Gerais (1977) and a PhD in Mathematics – University of Liverpool (1981). He is currently a professor at the Federal University of Minas Gerais, President of the Brazilian Mathematical Society from 1993 to 1997, reviewer – American Mathematical Society, ad-hoc consultant for the National Council for Scientific and Technological Development, ad-hoc consultant for the Coordination for the Improvement of Higher Education Personnel, representative of the area of Mathematics/Probability and Statistics at CAPES for the three-year period 2005/2007, member of the Technical-Scientific Council of CAPES for the three-year period 2005/2007, assistant coordinator of the area of Mathematics, Probability and Statistics at CAPES, three-year period 2007-2010; member of CA-Matemática CNPq, triennium 2010-2013; member of the scientific council – Union Matematica de America Latina y Caribe, ad-hoc consultant to the Ministry of Science and Technology, member of the Chamber of Exact Sciences and Materials of FAPEMIG for the biennium 2006/2007, consultant to the State Research Support Foundation of Minas Gerais, from the Araucária Foundation for Development Support. Scientific and Technological Institute of Paraná, the Research Support Foundation of the State of Rio de Janeiro and the Research Support Foundation of the State of São Paulo. He has experience in Mathematics, with emphasis on Theory of Singularities and Geometric Aspects of Holomorphic Foliations.

GEOMETRIC THEORY OF foliations and MATHEMATICAL ECONOMY

Within the scope of Economic Theory there is a strong interest in the behavior of aggregates, formed by the addition of several elementary functions of demand and supply. In turn, these elementary functions come from decision processes at the individual level. The standard example is the characterization of aggregate demand or excess demand markets. There is a relatively extensive bibliography on this subject, which contains several models, all of which have a common facet: the consideration of the same type of problem in Mathematics. In the project in question, we intend to approach some of these models and, here is the imponderable of this proposal, to try to build effective generalizations (perhaps applicable) of these, using methods derived from the Geometric Theory of Foliations. The interdisciplinary character of the project fits in the interface between Mathematics and Economics. On the mathematical side we find geometric problems, subject to optimization conditions and apparently very far from economic issues, while in the field of Economics there is the theory of aggregates, with its questions that naturally lead to geometric problems and the hypotheses that force the conditions of optimization.