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 $I$ band luminosity functions and colour-magnitude diagrams from HST imaging for eleven $0.2<z<0.6$ clusters observed at various stages of merging, and a comparison sample of five more relaxed clusters at similar redshifts. The characteristic magnitude $M^*$ evolves passively out to $z=0.6$, while the faint end slope of the luminosity function is $\alpha \sim -1$ at all redshifts. Cluster galaxies must have been completely assembled down to $M_I \sim -18$ out to $z=0.6$. 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 $z=0.6$. The blue galaxy fraction rises with redshift, especially at fainter absolute magnitudes. We observe bright blue galaxies in clusters at $z > 0.4$ 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 $M^*$. 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

On the Cost of Private Standards in Public Law

This is the published version

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