Swiss Alps - 2017

Paulo M. de Carvalho Neto is a Professor of Mathematics at the Federal University of Santa Catarina (UFSC) in Florianópolis, Brazil. He is also member of the Partial Differential Equations group at UFSC. Currently, he was (2016-2018) the organizer of the weekly Colloquium in Mathematics at his department, which is mainly addressed to graduate students.

 

In 2007 he obtained his undergraduate degree in mathematics at São Paulo State University (UNESP), receiving the title of best academic performance in the course. In 2009 he obtained his Master degree under the supervision of Gabriela Planas and in 2013 his Ph.D. under the supervision of Alexandre N. Carvalho, both from the University of São Paulo (USP). He also obtained a Spanish Ph.D. from University of Sevilla (US), under the supervision of Pedro Marín Rubio. During 2013 - 2015 he had a postdoctoral position at University of Campinas (UNICAMP) where he was a member of the Partial Differential Equations research group. Since then he has taught at Federal University of Santa Catarina.

Shortly, he has experience in Analysis and his research focuses are on theory of fractional calculus in abstract spaces, mainly in differential equations with time fractional derivatives, nonlinear dynamical systems, fluid dynamics and spectral theory of unbounded operators. 

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ACADEMIC BACKGROUND

  • Postdoctoral Researcher - UNICAMP - Brazil

  • Ph.D. in Mathematics - USP - Brazil

  • Ph.D. in Mathematics - US - Spain

  • Master Degree in Mathematics - USP - Brazil

  • Undergraduate Degree in Mathematics - UNESP - Brazil

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PERSONAL LINKS

UNIVERSITY ADDRESS

Department of Mathematics

Federal University of Santa Catarina

Campus Universitário Reitor João David Ferreira Lima

Trindade, 80040-900

Florianópolis - SC - Brazil 

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CONTACT INFORMATION

   Phone Number: +55 (48) 3721-3598

   Email: paulo.carvalho@ufsc.br

   Office: Room #203 in the Mathematics Building

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RESEARCH INTERESTS

  • Fluid Dynamics

    • Navier-Stokes equations;

    • Navier-friction boundary condition;

    • Inviscid limit.

  • Fractional Calculus

    • Mittag-Leffler functions;

    • Caputo and Riemann-Lioville derivatives;

    • Differential equations;

    • Fundamental properties.

  • Functional Analysis

    • Spectral Theory;

    • Sectorial and almost sectorial operators;

    • Fractional power of operators.

  • Nonlinear Dynamical Systems

    • Semigroups;

    • Atractors;

    • Pullback attractors.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world."

—Bertrand Russell (1919). "The Study of Mathematics". Mysticism and Logic: And Other Essays. Longman. p. 60. Chapter 4.

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