Mathematical Sciences Department
Levi L. Conant Lecture
Title: Fractional derivatives: Fourier, elephants, memory effects, viscoelastic materials, and anomalous diffusions
Speaker: Pablo Raúl Stinga, Iowa State University
Abstract: We all know how to compute one, two, three or more derivatives of differentiable functions, and how to integrate them. When calculus was being discovered, Leibniz introduced the idea of defining the derivative of order 1/2 of a function. Years later, Fourier came up with a general definition of a fractional derivative that would work for any function. We will unpack Fourier’s definition of fractional derivative (and fractional integral) using modern methods and present the Fundamental Theorem of Fractional Calculus. We will then show how fractional differential equations arise naturally in models of data science, viscoelastic materials in mechanics and anomalous diffusions in physics.
Bio: Pablo Raúl Stinga earned his Licenciatura en Ciencias Matemáticas degree at Universidad Nacional de San Luis, in San Luis, Argentina (2005). He earned his Máster en Matemáticas y Aplicaciones (2007) and his Doctorado en Matemáticas Doctor Europeus under the direction of José L. Torrea at Universidad Autónoma de Madrid, Spain (2010). He held postdoctoral research positions at Universidad de Zaragoza, Spain (2010) and Universidad de La Rioja, Spain (2011–2012). During the period 2012–2015, he was the R.H. Bing Fellow in Mathematics No.1 Instructor at The University of Texas at Austin, USA, where he worked as a postdoctoral researcher under the supervision of Luis A. Caffarelli. He is currently Professor at Iowa State University, USA. His research interests are in analysis, partial differential equations and nonlocal fractional equations.