Related papers: Cautionary remarks on the moduli space metric for …
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.
Muon reconstruction in the Daya Bay water pools would serve to verify the simulated muon fluxes and offer the possibility of studying cosmic muons in general. This reconstruction is, however, complicated by many optical obstacles and the…
Dark Matter could be a composite state of a confining sector with an approximate scale symmetry. We consider the case where the associated pseudo-Goldstone boson, the dilaton, mediates its interactions with the Standard Model. When the…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…
We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with…
The concept of the moduli space allows for a simple, universally applicable description of the low-energy dynamics of topological solitons. This description is remarkably insensitive to the properties of the underlying theory, whose details…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected…
We study vacua of moduli potential consisting of multiple contribution of modular forms in a finite modular symmetry. If the potential is given by a single modular form, the Minkowski vacuum is realized at the fixed point of the modular…
We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we use the Gleason-Iwasawa-Montgomery-Yamabe-Zippin structure…
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…
It is shown that the historical summary of the growth in size of N-body simulations as measured by particle number in this review is missing some key milestones. Size matters, because particle number with appropriate force smoothing is a…
We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and completeness and hence the measure theoretic requirements are…
This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
The dyonic 1/4-BPS states in 4D string theory with N=4 spacetime supersymmetry are counted by a Siegel modular form. The pole structure of the modular form leads to a contour dependence in the counting formula obscuring its duality…
We generalize the descriptions of vortex moduli spaces in \cite{Br} to more than one section with adiabatic constant $s$. The moduli space is topologically independent of $s$ but is not compact with respect to $C^\infty$ topology. Following…
Linear viscoelastic materials are commonly described by continuous relaxation spectra, yet practical measurements and simulations employ discrete Prony series. In the Laplace frequency domain, the distinction is well understood: rational…