Gunther Uhlmann

Gunther Alberto Uhlmann Arancibia (9 February 1952, Chile) is a mathematician whose research focuses on inverse problems and imaging, microlocal analysis, partial differential equations and invisibility.[1]

Gunther Uhlmann

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 Fellow[2] in 2010. He was an Invited Speaker at ICM[3] in Berlin in 1998[4] and a Plenary Speaker at International Congress on Industrial and Applied Mathematics in Zurich in 2007. He was named a Clay Senior Scholar[5] 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 Researcher[6] by ISI in 2004. He was awarded the Bôcher Memorial Prize in 2011 and the Kleinman Prize[7] also in 2011. In Fall 2011 he was a Rothschild Distinguished Visiting Fellow[8] at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. Uhlmann delivered the American Mathematical Society (AMS) Einstein Lecture in 2012.[9] He was awarded the Fondation Math'ematiques de Paris Research Chair for 2012–2013.[10] He was elected to the Washington State Academy of Sciences in 2012[11] and is also an AMS Fellow since 2012.[12] He was awarded a Simons Fellowship[13] 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. For 2021 he received the George David Birkhoff Prize of AMS-SIAM.[14]

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.[15] He and Richard Burt Melrose pioneered the study of paired Lagrangian distributions.[16] A striking application of this theory was given in the article with Allan Greenleaf on restricted X-ray transform.[17] He and John Sylvester made a major breakthrough in Calderón's inverse problem[18] that has led to many other developments[19] including the case of partial data.[20][21] 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.[22] and in higher dimensions with Plamen Stefanov and András Vasy.[23][24]

Uhlmann has also been interested in cloaking and invisibility. Uhlmann postulates the first mathematical equations to create invisible materials.[1] He and coauthors pioneered the idea of transformation optics for the case of electrostatics.[25][26] Surveys of results by Uhlmann and coauthors on cloaking can be found in.[27][28]

References
  1. Alonso, N: Un genio invisible, Revista Qué Pasa, 21 March 2013.
  2. SIAM Fellows: Class of 2010
  3. International Congress of Mathematicians, Berlin 1998
  4. Uhlmann, Gunther (1998). "Inverse boundary value problems for partial differential equations". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. III. pp. 77–86.
  5. Former Senior Scholars, Clay Mathematics Institute
  6. ISI Highly Cited Researcher
  7. Ralph E. Kleinman Prize
  8. Rothschild Visiting Professors, Isaac Newton Institute for Mathematical Sciences
  9. AMS Einstein Lecture
  10. Fondation Math'ematiques de Paris Research Chair Archived 23 March 2014 at the Wayback Machine
  11. Washington State Academy of Sciences Archived 8 December 2013 at the Wayback Machine
  12. List of Fellows of the American Mathematical Society, retrieved 2013-08-28.
  13. "Simons Fellows Awardees: Mathematics, Simons Foundation". Archived from the original on 18 July 2017. Retrieved 23 March 2014.
  14. George David Birkhoff Prize 2021
  15. "Light intensity distribution in conical refraction", Comm. on Pure and Appl. Math., 35 (1982), 69–80.
  16. "Lagrangian intersection and the Cauchy problem", Comm. on Pure and Appl. Math., 32 (1979), 483–519.
  17. Non-local inversion formulas for the X-ray transform, Duke Math. Journal, 58 (1989), 205–240.
  18. "A global uniqueness theorem for an inverse boundary value problem", Annals of Mathematics, 125 (1987), 153–169
  19. "Calderón's problem and electrical impedance tomography", Inverse Problems, 25th Anniversary Volume, 25 (2009), 123011.
  20. "The Calderón problem for partial Cauchy data", Annals of Mathematics, 22 (2007), 431–445
  21. "The Calderón problem with partial data in two dimensions", Journal American Math. Society, 23 (2010), 655–691
  22. "Two dimensional, compact, simple Riemannian manifolds are boundary distance rigid", Annals of Mathematics, 161 (2005), 1089–1106
  23. "A Local and Global Boundary Rigidity and the Geodesic X-ray Transform in the Normal Gauge", (2017)
  24. "Long-awaited mathematics proof could help scan Earth's innards", Nature News, (2017)
  25. "Anisotropic conductivities that cannot be detected by EIT", Physiological Measurement, 24 (2003), 413–420
  26. "On nonuniqueness for Calderón's inverse problem", Mathematical Research Letters, 10 (2003), 685–693
  27. "Cloaking devices, electromagnetic wormholes and transformation optics", SIAM Review 51 (2009), 3–33
  28. "Inverse problems and invisibility", Bulletin of the AMS 46 (2009), 55–97
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