Gunther Uhlmann

Gunther Alberto Uhlmann Arancibia (9 February 1952, Chile) 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 MIT where he received a Ph.D. 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. Since 2010 he has been on leave at the University of California, Irvine, as the Excellence in Teaching Endowed Chair.

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 [1] in 2010. He was an Invited Speaker at ICM [2] in Berlin in 1998 and a Plenary Speaker at International Congress on Industrial and Applied Mathematics in Zurich in 2007. He was named a Highly Cited Researcher[3] by ISI in 2004. He was awarded the Bôcher Memorial Prize in 2011 and the Kleinman Prize [4] also in 2011.

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.[5] He and Richard Burt Melrose pioneered the study of paired Lagrangian distributions.[6] A striking application of this theory was given in the article with Alan Greenleaf on restricted X-ray transform.[7] He and John Sylvester made a major breakthrough in Calderón's inverse problem[8] that has led to many other developments[9] including the case of partial data.[10][11] Another major breakthrough was the solution with Leonid Pestov of the boundary rigidity problem in two dimensions.[12] Uhlmann has also been interested in cloaking and invisibility. He and coauthors pioneered the idea of transformation optics for the case of electrostatics.[13][14] Surveys of results by Uhlmann and coauthors on cloaking can be found in [15][16].

References

  1. ^ SIAM Fellows: Class of 2010
  2. ^ International Congress of Mathematicians, Berlin 1998
  3. ^ ISI Highly Cited Researcher
  4. ^ Ralph E. Kleinman Prize
  5. ^ Light intensity distribution in conical refraction, Comm. on Pure and Appl. Math., 35 (1982), 69–80.
  6. ^ Lagrangian intersection and the Cauchy problem, Comm. on Pure and Appl. Math., 32 (1979), 483–519.
  7. ^ Non-local inversion formulas for the X-ray transform, Duke Math. Journal, 58 (1989), 205–240.
  8. ^ A global uniqueness theorem for an inverse boundary value problem, Annals of Math., 125 (1987), 153–169
  9. ^ Calderón's problem and electrical impedance tomography, Inverse Problems, 25th Anniversary Volume, 25 (2009), 123011.
  10. ^ The Calderón problem for partial Cauchy data, Annals of Math., 22 (2007), 431–445
  11. ^ The Calderón problem with partial data in two dimensions, Journal American Math. Society, 23 (2010), 655–691
  12. ^ Two dimensional, compact, simple Riemannian manifolds are boundary distance rigid, Annals of Math, 161 (2005), 1089–1106
  13. ^ Anisotropic conductivities that cannot be detected by EIT, Physiological Measurement, 24 (2003), 413–420
  14. ^ On nonuniqueness for Calderón's inverse problem, Mathematical Research Letters, 10 (2003), 685–693
  15. ^ Cloaking devices, electromagnetic wormholes and transformation optics, SIAM Review 51 (2009), 3–33
  16. ^ Inverse problems and invisibility, Bulletin AMS 46 (2009), 55–97

External links