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Jeremy Miller

Publications and source records attributed to Jeremy Miller.

61 records · Page 4Linked to original sources
arXiv2014

A practical, covariant puncture for second-order self-force calculations

Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the second-order gravitational self-force on the inspiraling small object. Recently, numerical puncture schemes have been formulated to calculate this force, and their essential analytical ingredients have been derived from first principles. However, the \emph{puncture}, a local representation of the small object's self-field, in each of these schemes has been presented only in a local coordinate system centered on the small object, while a numerical implementation will require the puncture in coordinates covering the entire numerical domain. In this paper we provide an explicit covariant self-field as a local expansion in terms of Synge's world function. The self-field is written in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable for both self-consistent and Gralla-Wald-type representations of the object's trajectory. We illustrate the local expansion's utility by sketching the procedure of constructing from it a numerically practical puncture in any chosen coordinate system.

gr-qc↗
arXiv2013

Homological stability for complements of closures

We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture to the case of connected manifolds of dimension at least 2 and give an explicit homological stability range.

math.AT↗
arXiv2013

Localization and homological stability of configuration spaces

In [Chu12], Church used representation stability to prove that the space of configurations of distinct unordered points in a closed manifold exhibit rational homological stability. A second proof was also given by Randal-Williams in [RW11] using transfer maps. We give a third proof of this fact using localization and rational homotopy theory. This gives new insight into the role that the rationals play in homological stability. Our methods also yield new information about stability for torsion in the homology of configuration spaces of points in a closed manifold.

math.AT↗
arXiv2013

Nonabelian Poincare duality after stabilizing

We generalize the nonabelian Poincare duality theorems of Salvatore in [Sal01] and Lurie in [Lur09] to the case of not necessarily grouplike E_n-algebras (in the category of spaces). We define a stabilization procedure based on McDuff's "brining points in from infinity" maps from [McD75]. For open connected parallelizable n-manifolds, we prove that, after stabilizing, the topological chiral homology of M with coefficients in an E_n-algebra A, is homology equivalent to Map^c(M,B^n A), the space of compactly supported maps to the n-fold classifying space of A. The two models of topological chiral homology used in this paper are Andrade's model from [And10] and Salvatore's from [Sal01].

math.AT↗
arXiv2011

Homological stability properties of spaces of rational J-holomorphic curves in P^2

In a well known work [Se], Graeme Segal proved that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding continuous mapping space through a range of dimensions increasing with degree. In this paper, we address if a similar result holds when other (not necessarily integrable) almost complex structures are put on projective space. We take almost complex structures that are compatible with the underlying symplectic structure. We obtain the following result: the inclusion of the space of based degree k J-holomorphic maps from P^1 to P^2 into the double loop space of P^2 is a homology surjection for dimensions j<3k-2. The proof involves constructing a gluing map analytically in a way similar to McDuff and Salamon in [MS] and Sikorav in [S] and then comparing it to a combinatorial gluing map studied by Cohen, Cohen, Mann, and Milgram in [CCMM].

math.SG↗
arXiv2009

Pomeron loop summation in perturbative QCD and the survival probability

The survival probability for exclusive diffractive Higgs production is calculated. The contribution of short distance interactions are taken into account, by summing over Pomeron loops in perturbative QCD. The summation is performed by developing an iterative technique to sum over loop diagrams with higher and higher generations of loops. The results show that the survival probability depends inversely on energy and is small for the LHC range of energies, and could be even less than 1 %.

hep-ph↗