Frieze patterns of numbers, introduced in the early 1970s by Coxeter, are currently attracting much interest due to connections with the recent theory of cluster algebras. The present survey aims to review the original work of Coxeter and the new developments around the notion of frieze, focusing on the representation theoretic, geometric and combinatorial approaches.

Given any ε > 0, we construct an orthonormal system of nk uniformly bounded polynomials of degree at most k on the unit sphere in Rm+1 where nk is bigger than 1 − ε times the dimension of the space of polynomials of degree at most k. Similarly, we construct an orthonormal system of sections of powers Ak of a positive holomorphic line bundle on a compact K¨ahler manifold with ca…

In this paper, we investigate the exactness of the Grassmannian Bernstein-Gel’fand-Gel’fand complexes introduced in a previous work of the author, and obtain some inequalities between some Hodge numbers of some irregular varieties. In particular, we obtain sharp lower bounds for the Hodge numbers of smooth subvarieties of Abelian varieties, as well as some improvements of results of Lazarsf…

We consider operators T : M0 → Z and T : M → Z, where Z is a Banach space and (M0,M) is a pair of Banach spaces belonging to a general construction in which M is defined by a ‘big-O’ condition and M0 is given by the corresponding ‘little-o’ condition. Prototype examples of such spaces M are given by ∞, weighted spaces of functions or their derivatives, bounded mean os…

Colleges and universities need to provide students with training and experience in (a) interdisciplinary research, (b) the fuzzy areas of responsible conduct of research, and (c) the mentor–mentee relationship. We developed workshops that combine the three content objectives— interdisciplinary research, responsible conduct of research, and mentor–mentee relationship, therefore promoting e…

The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalities for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal amount of smoothing, as well as a variant of that which describes quantitatively an improvement of the inequality as one gets away from certain characteristi…

This paper gives a simple criterion for a multiple Fourier series to be a Hilbert modular form.

In recent years, exciting scientific evidence has emerged highlighting the ecological importance of dead animals (i.e., carrion) and their consumption (i.e., scavenging), to the point that we could consider this the golden age of scavenging research. We now have a considerable body of theoretical and empirical work that indicates that scavenging is fundamental to properly understanding not only…

This article develops a theoretical framework to analyse options for financing infrastructure in developing countries. We build a basic model that gives motivations for using a combination of public finance, private debt, and private equity. The model is then extended in a number of ways to examine factors that are important for developing countries. We focus in particular on key institutional…

Grandmothers� availability for childcare has been shown to increase the labor force participation (LFP) and fertility of daughters. However, grandmothers� childcare availability depends highly on their LFP. When grandmothers work, intergenerational income transfers to their daughters may increase at the expense of time transfers (through childcare). Using a Two-stage Two-steps Least S…