Gunther Alberto Uhlmann Arancibia (9 February 1952, Chile) is a mathematician whose research focuses on inverse problems and , microlocal analysis, partial differential equations and invisibility.
Education and career Uhlmann studied mathematics as an undergraduate at the Universidad de Chile in Santiago, gaining his licenciatura degree in 1973. He continued his studies at MIT where he received a PhD in 1976. He held postdoctoral positions at MIT, Harvard and NYU, including a Courant Instructorship at the Courant Institute in 1977–1978. In 1980, he became Assistant Professor at MIT 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. Uhlmann was Finnish Distinguished Professor 2012–2017. He is currently also the Si-Yuan Professor at the Institute for Advanced Studies of the Hong Kong University of Science and Technology since 2014.
Awards and honors Uhlmann has received several honors for his research including a Sloan Fellowship in 1984 and a Guggenheim fellowship in 2001. In 2001 he was elected a Corresponding Member of the Chilean Academy of Sciences. He is a Fellow of the Institute of Physics since 2004. He was elected to the American Academy of Arts and Sciences in 2009 and a SIAM FellowSIAM Fellows: Class of 2010 in 2010. He was an Invited Speaker at ICMInternational Congress of Mathematicians, Berlin 1998 in Berlin in 1998 and a Plenary Speaker at International Congress on Industrial and Applied Mathematics in Zurich in 2007. He was named a Clay Senior Scholar at the Mathematical Sciences Research Institute (MSRI) at Berkeley in the Fall of 2010. In Fall 2010 he held the Chancellor Professorship at UC Berkeley. He was named a Highly Cited ResearcherISI Highly Cited Researcher by ISI in 2004. He was awarded the Bôcher Memorial Prize. in 2011 and the Kleinman PrizeRalph E. Kleinman Prize also in 2011. In Fall 2011 he was a Rothschild Distinguished Visiting Fellow at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. Uhlmann delivered the American Mathematical Society (AMS) Einstein Lecture in 2012.AMS Einstein Lecture He was awarded the Fondation Math'ematiques de Paris Research Chair for 2012–2013.Fondation Math'ematiques de Paris Research Chair He was elected to the Washington State Academy of Sciences in 2012Washington State Academy of Sciences and is also an AMS Fellow since 2012.List of Fellows of the American Mathematical Society, retrieved 2013-08-28. He was awarded a Simons Fellowship for 2013–2014. In 2013, he was elected Foreign Member of the Finnish Academy of Science and Letters. He gave a Plenary Lecture at the International Congress on Mathematical Physics in 2015 and a Plenary Lecture at the V Congreso Latinamericano de Matemáticos (CLAM) in 2016. In 2017 he was awarded the Solomon Lefschetz Medal by the Mathematical Council of the Americas. In the Fall of 2019, Uhlmann was a Clay Senior Scholar at MSRI, Berkeley. In 2021 he was awarded by AMS and SIAM the George David Birkhoff Prize.George David Birkhoff Prize 2021 In 2021, he also received a Simons Fellowship.List of 2021 Simons Fellows in Mathematics and Theoretical Physics In 2022 he was awarded the Doctor Honoris Causa by the University of Helsinki. In 2023 he was elected as a member of the National Academy of Sciences.NAS Election Uhlmann was awarded in 2025 the Doctor Honoris Causa of the University of Chile. In 2026 he will receive the Sven Berggren Prize of the Royal Physiographic Society of Lund.
Research 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."Light intensity distribution in conical refraction", Comm. on Pure and Appl. Math., 35 (1982), 69–80. He and Richard Burt Melrose pioneered the study of paired Lagrangian distributions."Lagrangian intersection and the Cauchy problem", Comm. on Pure and Appl. Math., 32 (1979), 483–519. A striking application of this theory was given in the article with Allan Greenleaf on restricted X-ray transform.Non-local inversion formulas for the X-ray transform, Duke Math. Journal, 58 (1989), 205–240. He and John Sylvester made a major breakthrough in Calderón's inverse problem"A global uniqueness theorem for an inverse boundary value problem", Annals of Mathematics, 125 (1987), 153–169 that has led to many other developments"Calderón's problem and electrical impedance tomography", Inverse Problems, 25th Anniversary Volume, 25 (2009), 123011. including the case of partial data."The Calderón problem for partial Cauchy data", Annals of Mathematics, 22 (2007), 431–445"The Calderón problem with partial data in two dimensions", Journal American Math. Society, 23 (2010), 655–691 Applications of this problem include Electrical resistivity tomography in geophysics and Electrical impedance tomography in medical imaging. Another major breakthrough was the solution of the boundary rigidity problem in two dimensions with Leonid Pestov"Two dimensional, compact, simple Riemannian manifolds are boundary distance rigid", Annals of Mathematics, 161 (2005), 1089–1106 and in higher dimensions with Plamen Stefanov and András Vasy."A Local and Global Boundary Rigidity and the Geodesic X-ray Transform in the Normal Gauge", (2017)"Long-awaited mathematics proof could help scan Earth's innards", Nature News, (2017)
Uhlmann has also been interested in cloaking and invisibility. Uhlmann postulates the first mathematical equations to create invisible materials.Alonso, N: Un genio invisible, Revista Qué Pasa, 21 March 2013. He and coauthors pioneered the idea of transformation optics for the case of electrostatics."Anisotropic conductivities that cannot be detected by EIT", Physiological Measurement, 24 (2003), 413–420"On nonuniqueness for Calderón's inverse problem", Mathematical Research Letters, 10 (2003), 685–693 Surveys of results by Uhlmann and coauthors on cloaking can be found in."Cloaking devices, electromagnetic wormholes and transformation optics", SIAM Review 51 (2009), 3–33"Inverse problems and invisibility", Bulletin of the AMS 46 (2009), 55–97
See also List of Guggenheim Fellowships awarded in 2001
References
External links
Home page at the University of Washington Webpage on the work of invisibility by G. Uhlmann and collaborators