A compactness result in approach theory with an application to the continuity approach structure

We establish a compactness result in approach theory which we apply to obtain a generalization of Prokhorov's Theorem for the continuity approach structure.Comment: 10 page

Hochschild cohomology, the characteristic morphism and derived deformations

A notion of Hochschild cohomology of an abelian category was defined by Lowen and Van den Bergh (2005) and they showed the existence of a characteristic morphism from the Hochschild cohomology into the graded centre of the (bounded) derived category. An element in the second Hochschild cohomology group corresponds to a first order deformation of the abelian category (Lowen and Van den Bergh, 2006). The problem of deforming single objects of the bounded derived category was treated by Lowen (2005). In this paper we show that the image of the Hochschild cohomology element under the characteristic morphism encodes precisely the obstructions to deforming single objects of the bounded derived category. Hence this paper provides a missing link between the above works. Finally we discuss some implications of these facts in the direction of a ``derived deformation theory''.Comment: 24 page

Economics in the Kingdom of Loathing: Analysis of Virtual Market Data

We analyze a unique data set from a massively-multiplayer online video game economy called The Kingdom of Loathing to assess the viability of these markets in conducting economic research. The data consist of every transaction in a market with over one million players over three years of real time. We find that 1) the game markets are efficient, 2) the complexity of the product determines information diffusion times, and 3) we can classify which and how players participate in trade.

On compact generation of deformed schemes

We obtain a theorem which allows to prove compact generation of derived categories of Grothendieck categories, based upon certain coverings by localizations. This theorem follows from an application of Rouquier's cocovering theorem in the triangulated context, and it implies Neeman's result on compact generation of quasi-compact separated schemes. We prove an application of our theorem to non-commutative deformations of such schemes, based upon a change from Koszul complexes to Chevalley-Eilenberg complexes.Comment: 21 page