Associate Professor, Department of Mathematics
Ignacio Uriarte-Tuero is an Associate Professor in the Department of Mathematics.
His research interests are in harmonic and complex analysis, geometric measure theory, potential theory and number theory. He has worked on quasiconformal maps in the plane — maps that model elasticity — where he proved, jointly with Michael Lacey and Eric Sawyer, a 16-year-old conjecture of Astala on Hausdorff measure distortion of quasiconformal maps. Separately, he obtained other related results such as the optimality of this conjecture.
He has worked on weighted norm inequalities which are certain inequalities for some integrals in which the measures are taken with respect to some inhomogeneous densities. He also proved the Nazarov-Treil-Volberg conjecture on a real variable characterization of the two weight norm inequality for the Hilbert transform — the most basic, but nontrivial case of interest in this field. This was done in a two-part paper: the first by Lacey, Sawyer, Shen and Uriarte-Tuero; the second by Lacey. He is also working on classical complex analysis, relations of number theory and harmonic analysis, and on Whitney extension problems — among other topics.
Uriarte-Tuero received his PhD from Yale University. He was a postdoctoral fellow at the University of Helsinki and then, at the University of Missouri. He was a full professor at Michigan State University before joining U of T.
Uriarte-Tuero was awarded the Sloan research fellowship and a National Science Foundation CAREER award.