On the Colmez conjecture for non-abelian CM fields

The Colmez conjecture relates the Faltings height of an abelian variety with complex multiplication by the ring of integers of a CM field E to logarithmic derivatives of Artin L-functions at s=0. In this paper, we prove that if F is any fixed totally real number field of degree [F:ℚ]≥3, then there are infinitely many effective, “positive density” sets of CM extensions E / F such that E/ℚ is non-abelian and the Colmez conjecture is true for E. Moreover, these CM extensions are explicitly constructed to be ramified at arbitrary prescribed sets of prime ideals of F. We also prove that the Colmez conjecture is true for a generic class of non-abelian CM fields called Weyl CM fields, and use this to develop an arithmetic statistics approach to the Colmez conjecture based on counting CM fields of fixed degree and bounded discriminant. We illustrate these results by evaluating the Faltings height of the Jacobian of a genus 2 hyperelliptic curve with complex multiplication by a non-abelian quartic CM field in terms of the Barnes double Gamma function at algebraic arguments. This can be viewed as an explicit non-abelian Chowla–Selberg formula. Our results rely crucially on an averaged version of the Colmez conjecture which was recently proved independently by Andreatta–Goren–Howard–Madapusi Pera and Yuan–Zhang.NFS with grants DMS-1162535 and DMS-1460766UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA

An intersectional perspective on the intergenerational transmission of trauma and state-perpetrated violence

We utilize intersectionality as the framework for analyzing and critiquing the literature on the intergenerational transmission of trauma in early childhood. In particular, we assess the extent to which the literature replicates the oppression of marginalized and minoritized children and families by deemphasizing traumas and traumatic processes that are attributable to interlocking systems of oppression. In addition, building on the emphasis on systems that is central to intersectionality, we assess the degree to which the literature engages with trauma perpetrated through formal social systems. We assert that an intersectional lens demands acknowledgement of state-perpetrated violence and that this acknowledgment is absent from the extant literature. To illustrate our argument, we present three structural analyses (“cases”) of state-perpetrated violence, leveraging life course theory and theories of historical and cultural trauma in addition to intersectionality theory to draw inferences about the intergenerational impacts of these cases. Through our analysis, we demonstrate how efforts to reduce contemporary state-perpetrated violence and repair the effects of historical state-perpetrated violence are well aligned with ongoing efforts in the public policy arena at promoting early childhood mental health and family thriving. We close with a proposed agenda for better integrating such efforts into research and policy

Identifying the transition between single and multiple mating of queens in fungus-growing ants.

Obligate mating of females (queens) with multiple males has evolved only rarely in social Hymenoptera (ants, social bees, social wasps) and for reasons that are fundamentally different from those underlying multiple mating in other animals. The monophyletic tribe of ('attine') fungus-growing ants is known to include evolutionarily derived genera with obligate multiple mating (the Acromyrmex and Atta leafcutter ants) as well as phylogenetically basal genera with exclusively single mating (e.g. Apterostigma, Cyphomyrmex, Myrmicocrypta). All attine genera share the unique characteristic of obligate dependence on symbiotic fungus gardens for food, but the sophistication of this symbiosis differs considerably across genera. The lower attine genera generally have small, short-lived colonies and relatively non-specialized fungal symbionts (capable of living independently of their ant hosts), whereas the four evolutionarily derived higher attine genera have highly specialized, long-term clonal symbionts. In this paper, we investigate whether the transition from single to multiple mating occurred relatively recently in the evolution of the attine ants, in conjunction with the novel herbivorous 'leafcutter' niche acquired by the common ancestor of Acromyrmex and Atta, or earlier, at the transition to rearing specialized long-term clonal fungi in the common ancestor of the larger group of higher attines that also includes the genera Trachymyrmex and Sericomyrmex. We use DNA microsatellite analysis to provide unambiguous evidence for a single, late and abrupt evolutionary transition from exclusively single to obligatory multiple mating. This transition is historically correlated with other evolutionary innovations, including the extensive use of fresh vegetation as substrate for the fungus garden, a massive increase in mature colony size and morphological differentiation of the worker caste