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Recognition of Research and a “Long-awaited” Finding

IAS Si Yuan Professor Gunther Uhlmann’s Advancement in His Research Career

2017 has been a rewarding year for Gunther Uhlmann, IAS Si Yuan Professor, who was featured in Nature earlier this year for a new mathematical finding. This past summer, he was also selected to receive the Solomon Lefschez Medal, another recognition for his contribution to research.

Uhlmann Receives the Solomon Lefschez Medal

In July 2017, Uhlmann was selected by the Mathematical Council of the Americas to receive the Solomon Lefschez Medal “for his universally recognized leadership of the rich and difficult field of inverse problems.”

Uhlmann’s research was commended for its ability to “combine sophisticated micro local analysis with an excellent taste for concrete physical problems.”

Explaining Physical Features with Mathematical Proof

In February, prior to the award, recent research by Uhlmann and his collaborators András Vasy and Plamen Stefanov was featured in Nature. These mathematicians proposed a solution to a geometric problem that may help determine the inner structure of a complex object, such as the Earth, by using wave data sampled on its surface.

Scientists study the Earth’s core by measuring the travel times of seismic waves generated in earthquakes. As measurements can only be made on the surface, they may be insufficient for reconstructing the interior. The major difficulties are that the core is unevenly distributed, and the speed of wave depends on both its location and its direction.

Mathematically, this problem—whether boundary data uniquely determine the interior of an object—is known as the boundary–rigidity conjecture. Uhlmann’s team has proved that determining the interior is indeed possible whenever the object satisfies suitable conditions. Knowing that the problem is solvable, they are working on numerical techniques for practical reconstructions.