Gunther Alberto Uhlmann Arancibia is a mathematician whose research focuses on inverse problems and imaging, microlocal analysis and partial differential equations.
Uhlmann studied mathematics as an undergraduate at the Universidad de Chile in Santiago, gaining his Licenciatura degree in 1973. He continued his studies at Massachusetts Institute of Technology where he received a Doctor of Philosophy in 1976.
He held postdoctoral positions at Massachusetts Institute of Technology, Harvard and New York University, including a Courant Instructorship at the Courant Institute in 1977–1978. In 1980, he became Assistant Professor at Massachusetts Institute of Technology and then moved in 1985 to the University of Washington. He has been the Walker Family Professor at the University of Washington since 2006.
During 2010-2012 he was on leave at the University of California, Irvine, as the Excellence in Teaching Endowed Chair.
The earlier work of Uhlmann was in microlocal analysis and propagation of singularities for equations with multiple characteristics, in particular in understanding the phenomenon of conical refraction. He and Richard Burt Melrose pioneered the study of paired Lagrangian distributions.
A striking application of this theory was given in the article with Alan Greenleaf on restricted X-ray transform. He and John Sylvester made a major breakthrough in Calderón"s inverse problem that has led to many other developments including the case of partial data.
Applications of this problem include Electrical resistivity tomography in geophysics and Electrical impedance tomography in medical imaging.
Another major breakthrough was the solution with Leonid Pestov of the boundary rigidity problem in two dimensions. Uhlmann has also been interested in cloaking and invisibility. He and coauthors pioneered the idea of transformation optics for the case of electrostatics.
Surveys of results by Uhlmann and coauthors on cloaking can be found in.
American Mathematical Society]
In 2001 he was elected a Corresponding Member of the Chilean Academy of Sciences. In 2013, he was elected Foreign Member of the Finnish Academy of Science and Letters.