Professor Hofmann's current research lies at the interface of harmonic analysis, partial differential equations, and geometric measure theory. In particular, using techniques of harmonic analysis, he studies the interaction between the geometry of the boundary of a domain, and the behavior of solutions of partial differential equations in the domain. His earlier work treated the theory of singular integrals and square functions, and their applications to partial differential equations.

Education

1988 Ph.D., University of Minnesota, Mathematics

1981 B.A., Washington University, St. Louis, Mathematics

Frequently Taught Courses

MATH 1400-2100 Calculus for Social and Life Sciences

(with C.Kenig, S.Mayboroda, and J.Pipher) Square function/Non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators, to appear, J. Amer. Math Soc.

(with J. M. Martell and S. Mayboroda) Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains, published online Int. Math. Research Notices 2013; doi: 10.1093/imrn/rnt002.

(with J. M. Martell and I. Uriarte-Tuero) Uniform Rectifiability and Harmonic Measure II:Poisson kernels in Lp imply uniform rectfiability, to appear Duke Math. J.

(with J. M. Martell) Uniform Rectifiability and Harmonic Measure I: Uniform rectifiability implies Poisson kernels in Lp, to appear Annales Scientifiques de L’ENS.

Local Tb Theorems and applications in PDE, Proceedings of the ICM Madrid, Vol. II, pp. 1375-1392, European Math. Soc., 2006.

(with P. Auscher, M. Lacey, A. McIntosh and P. Tchamitchian) The solution of the Kato square root problem for second order elliptic operators on Rn, Annals of Math. 156 (2002), pp 633-654.

(with A. McIntosh) The solution of the Kato problem in two dimensions, Proceedings of The Conference on Harmonic Analysis and PDE held in El Escorial, Spain in July 2000, Publ. Mat. Vol. extra, 2002 pp. 143-160.