On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Euler characteristics and elliptic curves

Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F∞ be the field obtained by adjoining to ℚ all p-power division points on E. Write G∞ for the Galois group of F∞ over ℚ. Assume that the complex L-series of E over ℚ does not vanish at s = 1. If p ⩾ 5, we make a precise conjecture about the value of the G∞-Euler characteristic of the Selmer group of E over F∞. If one makes a standard conjecture about the behavior of this Selmer group as a module over the Iwasawa algebra, we are able to prove our conjecture. The crucial local calculations in the proof depend on recent joint work of the first author with R. Greenberg.

Congruences between modular forms: Raising the level and dropping Euler factors

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida’s result accounts for congruences in terms of the value of an L-function, and Ribet’s result is related to the behavior of the period that appears there. Wiles’ theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at “nonminimal level” is obtained from one at “minimal level” by dropping Euler factors from the L-function.

Francesc Renart i Arús (1783-1853) i els orígens del teatre català vuitcentista

Estudi sobre l'obra dramàtica de Francesc Renart, inventari i inicis del sainet costumista català del Vuit-cents.

Deed of gift to Sarah Croswell, 1783 August 9

Handwritten list of furniture and an accompanying deed of gift between Andrew Croswell and Sarah Croswell.

Payment order for Daniel Parker on behalf of his son, 1783 July 10

Handwritten order to John Sale to pay scholarship funds to Daniel Parker for use by his son, signed by Charles Chauncey, John Clarke, Jonathan Williams, James Thwing, and Jacob Williams.

Corporation Dinner, 1783 May 16

Handwritten itemized list of costs for food and supplies purchased for a Corporation dinner held May 16, 1783.

I. Charlestown ferry bound volume, 1707-1806

This series contains sixty-nine documents related to the College's interest in the Charlestown ferry between 1707 and 1806 that were gathered together, arranged in chronological order, and pasted into a bound volume at an undetermined date. The majority of documents are leases and bonds with the ferrymen, as well as handwritten copies of Corporation petitions to the General Court regarding ferry fares and bridge development. The series also includes handwritten legal opinions composed by Levi Lincoln and Nathan Dane for the College analyzing the rights of the College to transportation-related income.