A Tour of Shape Formation
Imagine an airplane wing manufactured in a hyperbolic universe and imported into our Euclidean space. The incompatibility of the two geometries would be an obstacle for the relative ideal hyperbolic distances in the wing to be realized in the ambient Euclidean space. As a consequence, the wing would take on a deformed shape and be subject to internal stresses, making it not suitable for flying. This scenario, though imaginary, describes an everyday phenomenon known as prestrain in nonlinear elasticity. Here, prestrain refers to an incompatible ideal metric, and contrary to the above situation, it can play a positive role in nature and in applications. The math that explains how "good" the optimal shapes are when allowed to freely seek a strain minimizing deformation in space, combines some beautiful, old-standing questions in Riemannian Geometry with new techniques in Analysis and Calculus of Variations.
About the Speaker
Marta Lewicka is a professor of mathematics at the University of Pittsburgh. She specializes in nonlinear analysis, calculus of variations, mathematical theory of elasticity, conservation laws and reaction-diffusion equations. Dr. Lewicka earned Bachelor's and Master's degrees in mathematics in 1996 from the University of Gdansk, and a second Bachelor's degree in computer science in 1998 from Czestochowa University of Technology. She completed her Ph.D. in 2000 from the International School for Advanced Studies in Trieste, Italy under the supervision of Alberto Bressan. After postdoctoral research at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany and a term as L.E. Dickson Instructor at the University of Chicago, she joined the University of Minnesota faculty in 2005. She moved in 2010 to Rutgers University, and again in 2011 to Pittsburgh.
Marta Lewicka's research has been continuously supported by the National Science Foundation through many individual investigator grants including the prestigious NSF CAREER Award 2009-2015. In 2016 she gave an invited address at the AMS/MAA Joint Mathematical Meetings, in the area of nonlinear elasticity.
The Howard Rowlee Lecture Series is made possible through a generous donation by Mr. Howard E. Rowlee, Jr., a Lincoln resident and friend of the department, who has established a fund at the University of Nebraska Foundation to support research in mathematics. The Howard Rowlee Lecture is an annual event which seeks to bring internationally acclaimed scholars in the mathematical sciences to UNL to promote public understanding of mathematical research and to stimulate the environment for mathematics research at UNL.