Mayergoyz Invited to Speak at Symposium in France

Alford L. Ward Professor Isaak Mayergoyz (ECE) spoke at the Symposium on Trends in Applications of Mathematics to Mechanics (STAMM) which was held at the Université de Poitiers, Poitiers, France. His talk was titled, “Boundary Integral Equation Technique for Analysis of Plasmon Resonances in Nanoparticles and its Relation to the Riemann Hypothesis.”

In his talk, Mayergoyz covered the analysis of plasmon resonances in nanoparticles which can be stated as an eigenvalue problem for specific boundary integral equations of potential theory. In the 2D case, these integral equations have, for any boundary, real spectra with “mirror symmetry,” and their Fredholm determinants have the properties that have been proved or conjectured for the Riemann xi-function. This naturally suggests the idea to find such a boundary that the Fredholm determinant of the corresponding integral operator coincides with the xi-function. This approach can be regarded as one of the realizations of the spectral Hilbert-Polya conjecture originally stated for self-adjoint operators. Another related approach based on the J. Grommer theorem which reduces the Riemann hypothesis to polynomial analysis was discussed as well.

This year marked the 19^th STAMM hosted by the International Society for the Interaction of Mechanics and Mathematics (ISIMM). The workshop consisted of invited lectures, short communications, and poster presentations focused on mathematical modeling. The formulation and analysis of problems covered topics in physics, engineering, and other disciplines. The event took place from September 8-11, 2014.

For more information on STAMM ‘14, visit the symposium website.

Published September 17, 2014