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.

Recent results related Hochschild's relative homological theory with the Finitistic Dimension Conjecture, a central conjecture for finite dimensional algebras. In this talk we will use these results as a guide to present some classical homological ways to measure complexity of algebras, discussing their positive and negative aspects. Then we will understand how Hochschild's relative homological theory intends to measure the complexity of an extension of algebras and how his theory is related to the Finitistic Dimension Conjecture. Finally, we will present some ongoing results that aim to compute relative homological dimensions and provide some examples. This talk will be an exposition and most of the definitions will be presented and/or discussed.


This is an ongoing work with Prof. Iusenko and the talk will be in english.

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).