香蕉视频

Title: Universal Optimality of Hexagonal lattices

Abstract: It is well-known that the densest packing of the plane comes from the hexagonal lattice. A continuous version of this question is the universal optimality, asking whether the hexagonal lattice is the unique minimum configuration for each Gaussian potential. This deeper question is currently wide open. In the special case one restricts to the case of lattice configurations this can be rephrased as saying that the hexagonal lattice is the unique minimum for theta functions. This special case was established by Montgomery using a technique tailored to the space of lattice, which does not seem to extend to higher spaces of configuration. I will present a new proof of Montgomery's theorem obtained jointly with Naser Sardari and explain how our new strategy promises to adapt to higher spaces of configurations, which is ongoing work in progress.

听

Zoom link:

Meeting ID: 831 1853 9851

Passcode: 215516