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

Banned Books Week at RWU

You might remember this classic, bittersweet tale: A little girl named Fern raises a pig, Wilbur. Once full grown, Wilbur is sold to Fern’s uncle’s farm. Lonely in his barn, Wilbur befriends a spider named Charlotte. When Wilbur discovers he will soon be slaughtered, Charlotte has a plan. She weaves phrases into her web. “Some Pig,” she writes, “Humble, Radiant.” The community attributes the magical messages to Wilbur having a special gift and the pig’s life is spared, but Charlotte passes away soon after. Despite his grief, Wilbur finds comfort in his new friendship with Charlotte’s offspring

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

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

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

The Lower Dimensional Busemann-Petty Problem for Bodies with the Generalized Axial Symmetry

The lower dimensional Busemann-Petty problem asks, whether n-dimensional centrally symmetric convex bodies with smaller i-dimensional central sections necessarily have smaller volumes. The paper contains a complete solution to the problem when the body with smaller sections is invariant under rotations, preserving mutually orthogonal coordinate subspaces of fixed dimension. The argument relies on the notion of canonical angles between subspaces, spherical Radon transforms, properties of intersection bodies, and the generalized cosine transforms.Comment: 18 page