Bounded gaps between primes with a given primitive root

Fix an integer $g \neq -1$ that is not a perfect square. In 1927, Artin conjectured that there are infinitely many primes for which $g$ is a primitive root. Forty years later, Hooley showed that Artin's conjecture follows from the Generalized Riemann Hypothesis (GRH). We inject Hooley's analysis into the Maynard--Tao work on bounded gaps between primes. This leads to the following GRH-conditional result: Fix an integer $m \geq 2$. If $q_1 < q_2 < q_3 < \dots$ is the sequence of primes possessing $g$ as a primitive root, then $\liminf_{n\to\infty} (q_{n+(m-1)}-q_n) \leq C_m$, where $C_m$ is a finite constant that depends on $m$ but not on $g$. We also show that the primes $q_n, q_{n+1}, \dots, q_{n+m-1}$ in this result may be taken to be consecutive.Comment: small corrections to the treatment of \sum_1 on pp. 11--1

Summer of Shrew, Part 3: A Sly Conceit

In the third of a four-part series on Shakespeare\u27s The Taming of the Shrew, Daniel Pollack-Pelzner asks, what if Kate’s story isn’t the play’s only reality? Pollack-Pelzner explores how a drunken beggar and an earlier version of the script shift the brawling balances of the play and call into question who the real shrew is

Summer of Shrew, Part 2: Tamed? Really?

In the second of a four-part series on Shakespeare\u27s The Taming of the Shrew, Daniel Pollack-Pelzner argues that Shakespeare’s play raises challenging questions about the way we define gender roles, and the answers aren’t as obvious as they might seem

Deterring a Nuclear Iran: The Devil in the Details

Explores the technical requirements for a deterrence regime against Iran should it acquire a nuclear weapons capability. Considers red lines, treaty arrangements, force deployment and bases, military assistance to Iran's neighbors, and crisis management

A common phytoene synthase mutation underlies white petal varieties of the California poppy.

The California poppy (Eschscholzia californica) is renowned for its brilliant golden-orange flowers, though white petal variants have been described. By whole-transcriptome sequencing, we have discovered in multiple white petal varieties a single deletion leading to altered splicing and C-terminal truncation of phytoene synthase (PSY), a key enzyme in carotenoid biosynthesis. Our findings underscore the diverse roles of phytoene synthase in shaping horticultural traits, and resolve a longstanding mystery of the regaled golden poppy

Lin-Manuel Meets \u3cem\u3eMoana\u3c/em\u3e

In this article originally published in Public Books, Daniel Pollack-Pelzner wonders whether a Disney musical and a Lin-Manuel Miranda musical want the same thing

Quoting Shakespeare in the British Novel from Dickens to Wodehouse

Novelists heralded as Victorian Shakespeares frequently navigated the varied nineteenth-century practices of Shakespeare quotation (in the classroom in compilation books, in stage spoofs) to construct the relationship between narrator and character, and to negotiate the dialogue between Shakespeare\u27s voice and the voice of the novel. This chapter looks at three novelists whose practices intersect and contrast: George Eliot, who resists the Bardolatrous imputation of a Shakespearean character\u27s wisdom to its author by distinguishing her own characters\u27 inept Shakespeare quotations from her narrative voice; Thomas Hardy, who claims the authority of Shakespearean pastoral, regional language against the glib quotations of his more cosmopolitan characters; and a latter-day Victorian, P.G. Wodehouse, who plays the irreverent, defamiliarising gambits of Victorian Shakespeare burlesques against the educational and commonplace authority that Shakespeare quotations accrue

Summer of Shrew, Part 4: Which End’s Up?

In the last of a four-part series on Shakespeare\u27s The Taming of the Shrew, Daniel Pollack-Pelzner explores how expanding the range of the titular Shrew to include male characters is actually a return to its original meaning. Pollack-Pelzner focuses on a long-forgotten Renaissance sequel to Shrew (John Fletcher\u27s The Tamer Tamed) that takes the taming of men even further and turns its gender roles upside down