Generic uniqueness of expanders with vanishing relative entropy

We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that expanders with vanishing relative entropy are unique in a generic sense. This also implies that generically locally entropy minimising expanders are unique.Comment: 31 pages. Final version, to appear in Math. Annale

Low-energy spectrum of Toeplitz operators: the case of wells

In the 1980s, Helffer and Sj\"ostrand examined in a series of articles the concentration of the ground state of a Schr\"odinger operator in the semiclassical limit. In a similar spirit, and using the asymptotics for the Szeg\"o kernel, we show a theorem about the localization properties of the ground state of a Toeplitz operator, when the minimal set of the symbol is a finite set of non-degenerate critical points. Under the same condition on the symbol, for any integer K we describe the first K eigenvalues of the operator

Unemployment Insurance Application and Receipt: Findings on Demographic Disparities and Suggestions for Change

In this brief, we highlight research published in the October 2012 issue of Monthly Labor Review by Alix Gould-Werth and H. Luke Shaefer of the University of Michigan that examines the extent to which the likelihood of applying for, and of receiving unemployment insurance conditional on application, varies by education level and by racial and ethnic background. Second, we highlight findings showing how perceptions of ineligibility among those who fail to apply may vary by these demographic categories. This research demonstrates that low-educated and racial minority unemployed workers -- those who may need financial support most during periods without work -- are doubly disadvantaged in accessing unemployment insurance: not only do they report lower application rates, but the unemployed who do apply also report lower rates of receipt. Even though the authors' findings leave unanswered questions about the eligibility of non-applicants and the reasons applicants fail to access UI, their evidence suggests that increasing rates of application among disadvantaged populations would narrow the gap in benefit receipt. Thus, after summarizing the relevant findings, we offer recommendations for increasing application rates