Refined class number formulas and Kolyvagin systems

We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime $p$, each side of Darmon's conjectured formula (indexed by positive integers $n$) is "almost" a $p$-adic Kolyvagin system as $n$ varies. Using the fact that the space of Kolyvagin systems is free of rank one over $\mathbf{Z}_p$, we show that Darmon's formula for arbitrary $n$ follows from the case $n=1$, which in turn follows from classical formulas

Protest: A Teach-In

More than once in the last several years, Roger Williams\u27 waterfront campus has been the scene of peaceful, yet impactful dissent. Students have protested a lecture celebrating Christopher Columbus. They have gathered at the library to remember victims of the tragic shooting in Parkland, Florida and speak out against gun violence. They have laid down on campus concrete, signs with messages like, “We Can’t Breathe,” “No Justice, No Peace,” and “Black Lives Matter,” scattered amidst their chalk-outlined bodies

A Summer with National Center for Transgender Equality

Phoebe Thaler `19 spent her summer running around D.C–– from her office to protests, to rallies, to Capitol Hill. As an intern at National Center for Transgender Equality (NCTE), no two days were the same. The Supreme Court would hand out a decision or something would be happening on The Hill or the president would do something,” Thaler says, “and they’d just be like, ‘interns, get in an Uber––we’ll pay for it

Merck KGAA v. Integra Lifesciences I, Ltd.: Greater Research Protection for Drug Manufacturers

Merck sought protection under a statutory exemption from claims of patent infringement brought by Integra Lifesciences. The Court held unanimously that the safe harbor contained in 35 U.S.C. § 271(e)(1) protected the use of patented inventions used in preclinical research where the results were not submitted to the FDA. The Court\u27s interpretation of the safe harbor provision broadened protection for those engaged in drug research at a substantial cost to patent-holders

RWU Fall 2018 Poetry Slam

Students use poetry as a vehicle for voicing their passions, anger, and ideas for change, in the slam on Thursday, November 8. A new Spring course will offer an opportunity to continue this powerful work

Growing single crystals in silica gel

Two types of chemical reactions for crystal growing are discussed. The first is a metathetical reaction to produce calcium tartrate tetrahydrate crystals, the second is a decomplexation reaction to produce cuprous chloride crystals

Cultivating a Global Connection

A Hassenfeld Fellow’s transatlantic teaching experience demonstrates the impact of experiential learning through cultural exchange

On Gras conjecture for imaginary quadratic fields

In this paper we extend methods of Rubin to prove the Gras conjecture for abelian extensions of a given imaginary quadratic field k and prime numbers p which divide the number of roots of unity in k.Comment: accepted for publication in Canadian Mathematical Bulleti