Professor of Mathematics and Statistics receives Frontiers of Science Award
September 21, 2023 - Dani Rae Wascher
Matthew Blair, professor in the Department of Mathematics and Statistics at The University of New Mexico recently received a Frontiers of Science Award at the inaugural International Congress on Basic Science. This congress took place in Beijing during this summer.
The award was given to Blair and his coauthor, Christopher Sogge, a professor at Johns Hopkins University, to recognize the contribution of their research paper titled, “Logarithmic improvements in Lp bounds for eigenfunctions of the critical exponent in the presence of nonpositive curvature.” The paper was published in Inventiones Mathematicae, a top-ranked mathematics journal. Sogge traveled to Beijing for the congress and formally accepted the award on behalf of both of them.
“I fondly remember one of the eureka moments we had in the process, and from there all the other elements of the solution fell into place quite quickly. Given the struggle we went through, it meant a lot to be recognized with the award. At the time of writing, I felt it had been the best paper I have been involved in and I still believe that today,” expressed Blair.
The paper concerns so-called “standing waves,” waves that oscillate periodically in time about a fixed profile. They are analogous to solutions of the stationary Schrödinger equation appearing in quantum mechanics. It turns out that they provide a lens into much richer wave phenomena, i.e. the more researchers understand about standing waves, the more they can understand about wave propagation altogether. This is because in many cases, there are mathematical models that allow for a wave to be viewed as a sum of these standing waves. In order to take advantage of this, it is significant to study the behavior of these standing waves as they resonate at increasingly large frequencies.
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