The many topics of my past research are evidenced by the publication list in my CV. Currently I have the following projects underway:

(1) Bounding the response of anisotropic composites to electromagnetic fields, joint with my postdoc Kshiteej Deshmukh

(2) Recovering the volume fraction of composites from measurements in the time domain, joint with Boris Guervich, Ornella Mattei, and Mihai Putinar. Previously we had done this for the restricted case of conductivity (and related problems) but now we intend to do it for the far more applicable case of conductivity

(3) Designing domes as stable masonary structures, joint with Ada Amendola, Fernando Fraternali, Ornella Mattei, and Pierre Seppecher. Previously our studies were for arches.

(4) Establishing sets of fields that are closed under homogenization, joint with Yury Grabovsky. Thus, if we consider for simplicity the periodic context, if the fields take values in such a set, so do the average fields. The answer to this has widespread mathematical interest, not just to homogenization, but also to quasiconvexity, the calculus of variations, and the theory of shape memory materials.

(5) Bounding the response of composites to magnetic fields as governed by the Hall and Faraday coefficients, joint work with Christian Kern and Aaron Welters.

(6) Obtaining a counterexample to a conjecture of Molnar, joint with Aaron Welters. We have the proof and only need to write it up for publication.