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Moduli spaces of irregular singular connections
In the geometric version of the Langlands correspondence, irregular singular
point connections play the role of Galois representations with wild
ramification. In this paper, we develop a geometric theory of fundamental
strata to study irregular singular connections on the projective line.
Fundamental strata were originally used to classify cuspidal representations of
the general linear group over a local field. In the geometric setting,
fundamental strata play the role of the leading term of a connection. We
introduce the concept of a regular stratum, which allows us to generalize the
condition that a connection has regular semisimple leading term to connections
with non-integer slope. Finally, we construct a symplectic moduli space of
meromorphic connections on the projective line that contain a regular stratum
at each singular point.Comment: 53 pages. A new section (Section 4.4) has been added making precise
the relationship between formal types and isomorphism classes of formal
connections. Significant revisions and additions have also been made to
Sections 3.1 and 4.3 and the introduction to Section
Deep Luminosity Functions and Colour-Magnitude Relations for Cluster Galaxies at 0.2 < z < 0.6
We derive deep band luminosity functions and colour-magnitude diagrams
from HST imaging for eleven clusters observed at various stages of
merging, and a comparison sample of five more relaxed clusters at similar
redshifts. The characteristic magnitude evolves passively out to ,
while the faint end slope of the luminosity function is at all
redshifts. Cluster galaxies must have been completely assembled down to out to . We observe tight colour-magnitude relations over a
luminosity range of up to 8 magnitudes, consistent with the passive evolution
of ancient stellar populations. This is found in all clusters, irrespective of
their dynamical status (involved in a collision or not, or even within
subclusters for the same object) and suggests that environment does not have a
strong influence on galaxy properties. A red sequence luminosity function can
be followed to the limits of our photometry: we see no evidence of a weakening
of the red sequence to . The blue galaxy fraction rises with redshift,
especially at fainter absolute magnitudes. We observe bright blue galaxies in
clusters at that are not encountered locally. Surface brightness
selection effects preferentially influence the detectability of faint red
galaxies, accounting for claims of evolution at the faint end.Comment: 21 pages. A series of figures for individual clusters (the full
sample) will be made available on the MNRAS website. Accepted by MNRA
Morphological evolution in situ: Disk-dominated cluster red sequences at z ~ 1.25
We have carried out a joint photometric and structural analysis of red
sequence galaxies in four clusters at a mean redshift of z ~ 1.25 using optical
and near-IR HST imaging reaching to at least 3 magnitudes fainter than .
As expected, the photometry and overall galaxy sizes imply purely passive
evolution of stellar populations in red sequence cluster galaxies. However, the
morphologies of red sequence cluster galaxies at these redshifts show
significant differences to those of local counterparts. Apart from the most
massive galaxies, the high redshift red sequence galaxies are significantly
diskier than their low redshift analogues. These galaxies also show significant
colour gradients, again not present in their low redshift equivalents, most
straightforwardly explained by radial age gradients. A clear implication of
these findings is that red sequence cluster galaxies originally arrive on the
sequence as disk-dominated galaxies whose disks subsequently fade or evolve
secularly to end up as high S\'ersic index early-type galaxies (classical S0s
or possibly ellipticals) at lower redshift. The apparent lack of growth seen in
a comparison of high and low redshift red sequence galaxies implies that any
evolution is internal and is unlikely to involve significant mergers. While
significant star formation may have ended at high redshift, the cluster red
sequence population continues to evolve (morphologically) for several Gyrs
thereafter.Comment: Accepted by MNRA
Reckoning with Adjudication\u27s Exceptionalism Norm
Unlike rulemaking and judicial review, administrative adjudication is governed by a norm of exceptionalism. Agencies rarely adjudicate according to the Administrative Procedure Act’s formal adjudication provisions, and the statute has little role in defining informal adjudication or specifying its minimum procedural requirements. Due process has almost nothing to say about the matter.The result is that there are few uniform, cross-cutting procedural requirements in adjudication, and most hearings are conducted using procedures tailored for individual agencies or programs. This Article explores the benefits and costs of adjudication’s exceptionalism norm, an analysis that implicates the familiar tension between uniformity and specialization in the law. It argues that the exceptionalism norm overemphasizes specialization, at great cost.This Article urges a new regime designed to more properly balance the values of specialization and uniformity. The proposal contemplates that as in rulemaking, the project would entail an interbranch effort to protect fundamental rights and promote institutional integrity while preserving space for needed agency discretion
Reckoning with Adjudication’s Exceptionalism Norm
Unlike rulemaking and judicial review, administrative adjudication is governed by a norm of exceptionalism. Agencies rarely adjudicate according to the Administrative Procedure Act’s formal adjudication provisions, and the statute has little role in defining informal adjudication or specifying its minimum procedural requirements. Due process has almost nothing to say about the matter. The result is that there are few uniform, cross-cutting procedural requirements in adjudication, and most hearings are conducted using procedures tailored for individual agencies or programs. This Article explores the benefits and costs of adjudication’s exceptionalism norm, an analysis that implicates the familiar tension between uniformity and specialization in the law. It argues that the exceptionalism norm overemphasizes specialization, at great cost. This Article urges a new regime designed to more properly balance the values of specialization and uniformity. The proposal contemplates that as in rulemaking, the project would entail an interbranch effort to protect fundamental rights and promote institutional integrity while preserving space for needed agency discretion
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