Foreigners and the City: An Historiographical Exploration for the Early Modern Period

This paper will focus on the physical traces left by different minorities in the European city of the early modern age. Looking to the urban context in the main important ports and commercial centers we can find violent conflicts, traditional uses, as well as new urban strategies by the governors to keep together (for economic and social purposes) city-dwellers and foreigners. The invention of specific buildings and the effect on the architectural language is often quite visible and a mean of cultural exchanges.City, History of Architecture, Modern Age, Foreigners, Minorities

Stability of K\"ahler-Ricci flow in the space of K\"ahler metrics

In this paper, we prove that on a Fano manifold $M$ which admits a K\"ahler-Ricci soliton (\om,X), if the initial K\"ahler metric \om_{\vphi_0} is close to \om in some weak sense, then the weak K\"ahler-Ricci flow exists globally and converges in Cheeger-Gromov sense. Moreover, if \vphi_0 is also $K_X$-invariant, then the weak modified K\"ahler-Ricci flow converges exponentially to a unique K\"ahler-Ricci soliton nearby. Especially, if the Futaki invariant vanishes, we may delete the $K_X$-invariant assumption. The methods based on the metric geometry of the space of the K\"ahler metrics are potentially applicable to other stability problem of geometric flow near a critical metric.Comment: 28 pages, 1 figure

D-branes at Singular Curves of Calabi-Yau Compactifications

We study the Gepner model description of D-branes in Calabi-Yau manifolds with singular curves. From a geometrical point of view, the resolution of singularities leads to additional homology cycles around which branes can wrap. Using techniques from conformal field theory we address the construction of boundary states for branes wrapping additional 3-cycles on the resolved Calabi-Yau manifold. Explicit formulas are provided for Z_2 singular curves.Comment: 25 pages, late

Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms

In this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at 0 of Mather's $\beta$ function, thus providing a negative answer to a question asked by K. Siburg in \cite{Siburg1998}. However, we show that equality holds if one considers the asymptotic distance defined in \cite{Viterbo1992}.Comment: 21pp, accepted for publication in Geometry & Topolog

Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary

Kerckhoff and Storm conjectured that compact hyperbolic n-orbifolds with totally geodesic boundary are infinitesimally rigid when n>3. This paper verifies this conjecture for a specific example based on the 4-dimensional hyperbolic 120-cell.Comment: 9 page

Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds

We compute all loop topological string amplitudes on orientifolds of local Calabi-Yau manifolds, by using geometric transitions involving SO/Sp Chern-Simons theory, localization on the moduli space of holomorphic maps with involution, and the topological vertex. In particular we count Klein bottles and projective planes with any number of handles in some Calabi-Yau orientifolds.Comment: 40 pages, 18 figures, some corrections in section