Preperiodic points and unlikely intersections

In this article, we combine complex-analytic and arithmetic tools to study the preperiodic points of one-dimensional complex dynamical systems. We show that for any fixed complex numbers a and b, and any integer d at least 2, the set of complex numbers c for which both a and b are preperiodic for z^d+c is infinite if and only if a^d = b^d. This provides an affirmative answer to a question of Zannier, which itself arose from questions of Masser concerning simultaneous torsion sections on families of elliptic curves. Using similar techniques, we prove that if two complex rational functions f and g have infinitely many preperiodic points in common, then they must have the same Julia set. This generalizes a theorem of Mimar, who established the same result assuming that f and g are defined over an algebraic extension of the rationals. The main arithmetic ingredient in the proofs is an adelic equidistribution theorem for preperiodic points over number fields and function fields, with non-archimedean Berkovich spaces playing an essential role.Comment: 26 pages. v3: Final version to appear in Duke Math.

Special curves and postcritically-finite polynomials

We study the postcritically-finite (PCF) maps in the moduli space of complex polynomials $\mathrm{MP}_d$. For a certain class of rational curves $C$ in $\mathrm{MP}_d$, we characterize the condition that $C$ contains infinitely many PCF maps. In particular, we show that if $C$ is parameterized by polynomials, then there are infinitely many PCF maps in $C$ if and only if there is exactly one active critical point along $C$, up to symmetries; we provide the critical orbit relation satisfied by any pair of active critical points. For the curves $\mathrm{Per}_1(\lambda)$ in the space of cubic polynomials, introduced by Milnor (1992), we show that $\mathrm{Per}_1(\lambda)$ contains infinitely many PCF maps if and only if $\lambda=0$. The proofs involve a combination of number-theoretic methods (specifically, arithmetic equidistribution) and complex-analytic techniques (specifically, univalent function theory). We provide a conjecture about Zariski density of PCF maps in subvarieties of the space of rational maps, in analogy with the Andr\'e-Oort Conjecture from arithmetic geometry.Comment: Final version, appeared in Forum of Math. P

The Durham difference: considering our context

This article reflects on the experience of Durham University Library staff in promoting services as part of undergraduate induction. It challenges the perception that all methods of marketing are equally valuable to all institutions and explores some alternatives

Canonical transforming growth factor-β signaling regulates disintegrin metalloprotease expression in experimental renal fibrosis via miR-29

Fibrosis pathophysiology is critically regulated by Smad 2– and Smad 3–mediated transforming growth factor-β (TGF-β) signaling. Disintegrin metalloproteases (Adam) can manipulate the signaling environment, however, the role and regulation of ADAMs in renal fibrosis remain unclear. TGF-β stimulation of renal cells results in a significant up-regulation of Adams 10, 17, 12, and 19. The selective Smad2/3 inhibitor SB 525334 reversed these TGF-β–induced changes. In vivo, using ureteral obstruction to model renal fibrosis, we observed increased Adams gene expression that was blocked by oral administration of SB 525334. Similar increases in Adam gene expression also occurred in preclinical models of hypertension-induced renal damage and glomerulonephritis. miRNAs are a recently discovered second level of regulation of gene expression. Analysis of 3′ untranslated regions of Adam12 and Adam19 mRNAs showed multiple binding sites for miR-29a, miR-29b, and miR-29c. We show that miR-29 family expression is decreased after unilateral ureter obstruction and this significant decrease in miR-29 family expression was observed consistently in preclinical models of renal dysfunction and correlated with an increase in Adam12 and Adam19 expression. Exogenous overexpression of the miR-29 family blocked TGF-β–mediated up-regulation of Adam12 and Adam19 gene expression. This study shows that Adams are involved in renal fibrosis and are regulated by canonical TGF-β signaling and miR-29. Therefore, both Adams and the miR-29 family represent therapeutic targets for renal fibrosis

No IR? No Problem: The Resourceful Librarian’s Guide to Archiving Digitized Government Publications with the Internet Archive

This poster illustrates our practice and process of using the Internet Archive (IA) as a repository for digitized government publications. It shows how libraries without an institutional repository, or those that have an IR but lack support for uploading depository content, can still participate in digitization and preservation programs. By doing so, the library can highlight the value of its depository collection

The New Orleans Museum of Art: Managing the Collection

An internship experience in the Office of the Registrar and Collections Management at the New Orleans Museum of Art is reviewed alongside discussion of the Museum’s history, structure, and permanent collection, in addition to analyses of the organization’s finances and its institutional strengths, weaknesses, opportunities and threats. Discussion topics also include the intern’s experience, best practices in similar institutions, and a conclusion with recommendations made by the intern