Monday, October 21, 2019 at 4:15pm to 5:15pm
Room : 2 - 147 182 memorial Drive, MIT Building 2, Cambridge, MA, 02142
Featured Speaker : Eitan Bachmat (Ben - Gurion University)
Title : Probability, (Lorentzian) geometry and optimization in (low and) high dimension
We will consider a very basic relation between certain resource allocation problems and an abstract notion of optical lenses. As a special case, we will consider airplane boarding with a group of "slow" passengers and a group of "fast" passengers. The analysis and optimization of boarding in this scenario will lead us to consider the statistics of heaviest increasing subsequences and on the other hand to construct thick "gravitational lenses for electrons" (using fairy dust) and flat surfaces in the polynuclear growth model. Finally, we will note a concentration of measure result for "critical gravitational lenses" in high dimensional Minkowski space. This shows that it is possible to speed up "high dimensional projects" with very few resources. All the "terms" will be explained, and we will present several interesting problems.