We study experimentally and theoretically a cold trapped Bose gas under critical rotation, i.e., with a rotation frequency close to the frequency of the radial confinement. We identify two regimes: the regime of explosion where the cloud expands to infinity in one direction, and the regime where the condensate spirals out of the trap as a rigid body. The former is realized for a dilute cloud, a...

Abstract. We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around its limit. The method is based on a coupling argument, strong integrability estimates on the ...

Metapopulation models have been used to better understand the conditions necessary for the persistence of the metapopulation. In this paper, we study a stochastic patch occupancy model that incorporates variation in quality and connectivity of the habitat patches. Two important assumptions are imposed in our analysis. Firstly, the distance between patches has a special form. This amounts to ass...

A More Sums Than Differences (MSTD) set is a set A for which |A+A| > |A−A|. Martin and O’Bryant proved that the proportion of MSTD sets in {0, 1, . . . , n} is bounded below by a positive number as n goes to infinity. Iyer, Lazarev, Miller and Zhang introduced the notion of a generalized MSTD set, a set A for which |sA− dA| > |σA − δA| for a prescribed s + d = σ + δ. We offer efficient construc...

A Pick function of d variables is a holomorphic map from Πd to Π, where Π is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series ∑∞ n=1 ρnz −n with real numbers ρn that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences {ρn} can occur. We give an extension ...

I recently discussed these questions with Edward Frenkel, Berkeley mathematics professor and author of “Love and Math: The Heart of Hidden Reality.” “We have many ways to connect to infinity: through art, through poetry, through love,” explained Dr. Frenkel. “But mathematics gives us perhaps the most cerebral and logical way to connect to the infinite. So in this day and age, when we tend to pu...