As part of the Society for Industrial and Applied Mathematics (SIAM) Visiting Lecturer Program, Irene Fonseca will be at IUP on April 20, 2012, to give three presentations.

“Variational Methods in Materials Science and Image Processing”

Time: 1:25–2:15 p.m.

Location: Pratt Auditorium

Several questions in applied analysis motivated by issues in computer vision, physics, materials sciences, and other areas of engineering may be treated variationally leading to higher order problems and to models involving lower dimension density measures. Their study often requires state-of-the-art techniques, new ideas, and the introduction of innovative tools in partial differential equations, geometric measure theory, and the calculus of variations.

In this talk, it will be shown how some of these questions may be reduced to well-understood first order problems, while, in others, the higher order plays a fundamental role. Applications to phase transitions and to the equilibrium of foams under the action of surfactants, imaging, micromagnetics, thin films, and quantum dots will be addressed.

“Careers in Mathematics”

Time: 2:45–3:45 p.m.

Location: Stright Hall, room 226

Fonseca will speak to students about careers in mathematics.

“Variational Methods for Crystal Surface Instability”

Time: 4:00–4:50 p.m.

Location: Stright Hall, room 226

Using the calculus of variations, it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy. In addition, short-time existence, uniqueness, and regularity for an anisotropic surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short-time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

Irene Fonseca is president-elect of SIAM, Mellon College of Science professor of Mathematics at Carnegie-Mellon University, and director of the Center for Nonlinear Analysis.

Department of Mathematics