The symplectic Deligne-Mumford stack associated to a stacky polytope

We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic Deligne-Mumford stack associated to the stacky polytope. Then we establish a relation between stacky polytopes and stacky fans: the stack associated to a stacky polytope is equivalent to the stack associated to a stacky fan if the stacky fan corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic

The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Gesture for generalization: Gesture facilitates flexible learning of words for actions on objects

Verb learning is difficult for children (Gentner, 1982), partially because children have a bias to associate a novel verb not only with the action it represents, but also with the object on which it is learned (Kersten & Smith, 2002). Here we investigate how well 4- and 5-year-old children (N=48) generalize novel verbs for actions on objects after doing or seeing the action (e.g., twisting a knob on an object) or after doing or seeing a gesture for the action (e.g., twisting in the air near an object). We find not only that children generalize more effectively through gesture experience, but also that this ability to generalize persists after a 24-hour delay

Search for a scalar top quark using the OPAL detector

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