Professor Receives Praise for 40 Year Old Problem

An anonymous reader writes "The Kansas City Star is reporting that Steven Hofmann is in line to receive accolades from his peers this coming year in Madrid, Spain for solving a mathematical problem that has baffled mathematicians for over 40 years. Hofmann, a professor at the University of Missouri-Columbia, solved the 3 dimensional version of the 'Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds' (say that 10 times fast!). From the article: 'For three years, starting in 1996, Hofmann worked on the problem for two to eight hours every day [...] Hofmann said the solution could allow mathematicians to better describe the behavior of waves traveling through a medium that changes over time. But beyond that, he said, it is impossible for him to explain all the real-world applications.'"

Comments

Re:A nice little article

[alicenextdoor]

The abstract of the paper in question: "We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis, we establish that the domain of the square root of a complex uniformly elliptic operator L = div(A) with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate Lf2 f2. We note, in particular, that for such operators, the Gaussian hypothesis holds always in two dimensions."

No, I don't understand it, either! Something tells me this is one of those classic problems that you just can't explain in words of one syllable...

Re:Nobel prize for physics!

[0xC0FFEE]

That's effectively the nearest equivalent except for a few differences. First among them is that the price is given to people _under_ 40. Second the price is given every 4 years. So the Fields is way more difficult to get because of those additional constraints.