L' ospedale dei Cavalieri a Rodi

An article discussing the history and architecture of the hospital that was used by the Order of St. John in Rhodes, Greece.peer-reviewe

Harpur Palate, Volume 4 Issue 2, Winter 2005

Contributors: Gail Waldstein | Ryan G. Van Cleave | John W. Evans | J. Lorraine Brown | Maria Fire | Roy Kesey | Marvin Bell | George Tucker | Stan Sanvel Rubin | Kara D\u27Angelo | Travis Gearhart | Lee K. Abbott | Kristin Abraham | Jonathan Crimmins | Anne Keefe | Dani Rado | Sascha Feinstein | Ronald F. Currie, Jr. | Hal Sirowitz | Matthew Byrne | Sue William Silverman | Michael Hettich | Bruce Holland Rogers | Grace Cavalieri | Ron McFarland | Dara Cerv | Raymond P. Hammond | Doug Ramspeck | R. L. Futrell | Francine M. Tolf | Shane Seely | Candace Black | Russell Rowland | Joan Connor

A geometric perspective on the piecewise polynomiality of double Hurwitz numbers

We describe double Hurwitz numbers as intersection numbers on the moduli space of curves. Assuming polynomiality of the Double Ramification Cycle (which is known in genera 0 and 1), our formula explains the polynomiality in chambers of double Hurwitz numbers, and the wall crossing phenomenon in terms of a variation of correction terms to the {\psi} classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle.Comment: 15 pages, 5 figure

Hodge-type integrals on moduli spaces of admissible covers

We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation for this work comes from Bryan and Pandharipande's recent work on the local GW theory of curves, where analogouos intersection numbers, computed on Moduli Spaces of Relative Stable Maps, are the structure coefficients for a Topological Quantum Field Theory. Admissible Covers provide an alternative compactification of the Moduli Space of Maps, that is smooth and doesn't contain boundary components of excessive dimension. A parallel, yet different, TQFT, can then be constructed. In this paper we compute, using localization, the relevant Hodge integrals for admissible covers of a pointed sphere of degree 2 and 3, and formulate a conjecture for general degree. In genus 0, we recover the well-known Aspinwall Morrison formula in GW theory.Comment: This is the version published by Geometry & Topology Monographs on 21 September 200

Polynomiality, Wall Crossings and Tropical Geometry of Rational Double Hurwitz Cycles

We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon observed for double Hurwitz numbers, such cycles are piecewise polynomial in the entries of the special ramification; the chambers of polynomiality and wall crossings have an explicit and "modular" description. A main goal of this paper is to simultaneously carry out this investigation for the corresponding objects in tropical geometry, underlining a precise combinatorial duality between classical and tropical Hurwitz theory