Seminarios

 We study the assignment of indivisible goods to individuals when monetary transfers are not allowed. Previous literature has mainly focused on efficiency (from both ex-ante and ex-post perspectives) and individually fair assignments. As a result, egalitarian concerns have been overlooked. We draw inspiration from the assignment of apartments in housing cooperatives, where families consider egalitarianism of assignments as a first-order requirement. Specifically, they aim to avoid situations where some families receive their most preferred apartments while others are assigned options ranked very low in their preferences. Building on Rawls' concept of fairness, we introduce the notion of Rawlsian assignment. We prove that a unique Rawlsian assignment always exists. Furthermore, the Rawlsian rule is efficient and anonymous. To illustrate our analysis, we use preference data from housing cooperatives. We show that the Rawlsian rule substantially improves, from an egalitarian perspective, both the probabilistic serial rule, and the rule currently used to assign apartments in the housing cooperatives.

en coautoría con Tom Demeulemeester.

Sea S una superficie compacta, sin borde, orientable y de género g mayor que 1. Una estructura hiperbólica en S es un atlas de cartas al plano hiperbólico tal que los cambios de cartas son isometrías. El espacio de Teichmüller de S es el espacio de estructuras hiperbólicas en S, módulo isotopías. Este espacio admite una topología natural (homeomorfa a R^{6g-6}), pero soporta distintas geometrías: la de Teichmüller, la de Weil Petersson, la de Thurston. En esta charla nos concentraremos en la tercera, discutiendo un resultado de Thurston que brinda ejemplos explícitos de algunas de sus geodésicas. Luego discutiremos avances de un proyecto en progreso junto a X. Dai, B. Pozzetti y A. Wienhard en donde intentamos generalizar estos resultados al espacio de superficies proyectivas (es decir, cuando permitimos que nuestras cartas locales tengan por codominio el plano proyectivo).