Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.
Lecture announcement
About the lecturer: Graeme Milton earned his B.Sc. (1980) and M.Sc. (1982) in Physics from the University of Sydney. He completed his Ph.D. in Physics at Cornell University in 1985 (with Michael Fisher), working in statistical physics and composite materials. Following this, he was a Weingart Fellow at the California Institute of Technology from 1984 to 1986. He then joined the Courant Institute of Mathematical Sciences, remaining until 1994, when he moved to the University of Utah as a Full Professor. He has served as a Distinguished Professor there since 1999 and was recently named Distinguished Professor Emeritus. His research has made significant contributions to the theory of composite materials, metamaterials, including work on electromagnetic and acoustic scattering, variational principles, and bounds on material properties. He has also explored theoretical limits of cloaking and the mechanics of advanced engineered materials. Graeme Milton’s most prestigious recognitions include an invited lecture at the International Congress of Mathematicians (1998), the Packard Fellowship (1988–93), the Sloan Research Fellowship (1988), the Ralph E. Kleinman Prize (2003) and SIAM Fellowship (2009) from the Society for Industrial and Applied Mathematics, the William Prager Medal (2007), the Rolf Landauer Medal (2012), and the Levi-Civita Prize (2015).
Lecture abstract: 3-d printing gives us unprecedented ability to tailor microstructures to achieve desired goals. From the mechanics perspective one would like, for example, to know how to design structures that guide stress, in the same way that conducting fibers are good for guiding current. In that context the natural question is: what are the possible pairs of (average stress, average strain) that can exist in the material. A grander question is: what are the possible effective elasticity tensors that can be achieved by structuring an isotropic material with known moduli. This is a highly non-trivial problem. Here we review some of the progress that has been made on this question, and we discuss some open problems. This is joint work with Marc Briane, Mohammed Camar Eddine, and Davit Harutyunyan.