Harvard University

Radar data from both Greenland and Antarctica show folds and other disruptions to the stratigraphy of the deep ice. The mechanisms by which stratigraphy deforms are related to the interplay between ice flow and topography. Here we show that when ice flows across valleys or overdeepenings, viscous overturnings called Moffatt eddies can develop. At the base of a subglacial valley, the shear on the valley walls is transfered through the ice, forcing the ice to overturn. To understand the formation of these eddies, we numerically solve the non-Newtonian Stokes equations with a Glen's law rheology to determine the critical valley angle for the eddies to form. The decrease in ice viscosity with shear enhances shear localization and, therefore, Moffatt eddies form in smaller valley angles (steeper slopes) than in a fluid that does not localize shear, such as a Newtonian fluid. When temperature is incorporated into the ice rheology, the warmer basal ice is less viscous and eddies form in larger valley angles (shallower slopes) than in isothermal ice. We apply our simulations to the Gamburtsev Subglacial Mountains and solve for the ice flow over radar-determined topography. These simulations show Moffatt eddies on the order of 100 meters tall in the deep subglacial valleys.

The stability of structures continues to be scientifically fascinating and technically important.  Shell buckling emerged as one of the most challenging nonlinear problems in mechanics more than fifty years ago when it was intensively studied.  It has returned to life with new challenges motivated not only by structural applications but also by developments in the life sciences and in soft materials.  It is not at all uncommon for slightly imperfect thin cylindrical shells under axial compression or spherical shells under external pressure to buckle at 20% of the buckling load of the perfect shell.  A historical overview of shell buckling will be presented followed by a discussion of recent work by the speaker and his collaborators on the buckling of spherical shells.  Experimental and theoretical work will be described with a focus on imperfection-sensitivity and on viewing the phenomena within the larger context of nonlinear stability. 

Let X be a complex algebraic variety containing a point x. One of the central ideas of deformation theory is that the local structure of X near the point x can be encoded by a differential graded Lie algebra. In this talk, Jacob Lurie will explain this idea and discuss some generalizations to more exotic contexts.

Since their introduction, Shimura varieties have proven to be important landmarks sitting right at the crossroads between algebraic geometry, number theory and representation theory. In this talk, starting from the yoga of motives and Hodge theory, we will try to motivate Deligne's construction of Shimura varieties, and briefly survey some of their zoology and basic properties. I may also say something about the links to automorphic forms, or their integral canonical models.

This paper uses data on house transactions in the state of Massachusetts over the last 20 years

to show that houses sold after foreclosure, or close in time to the death or bankruptcy of at least

one seller, are sold at lower prices than other houses. Foreclosure discounts are particularly large on

average at 27% of the value of a house. The pattern of death-related discounts suggests that they may

result from poor home maintenance by older sellers, while foreclosure discounts appear to be related

to the threat of vandalism in low-priced neighborhoods. After aggregating to the zipcode level and

controlling for regional price trends, the prices of forced sales are mean-reverting, while the prices

of unforced sales are close to a random walk. At the zipcode level, this suggests that unforced sales

take place at approximately ecient prices, while forced-sales prices re

ect time-varying illiquidity in

neighborhood housing markets. At a more local level, however, we nd that foreclosures that take

place within a quarter of a mile, and particularly within a tenth of a mile, of a house lower the price

at which it is sold. Our preferred estimate of this eect is that a foreclosure at a distance of 0.05 miles

lowers the price of a house by about 1%.

Let L be a positive definite lattice. There are only finitely many positive definite lattices

L' which are isomorphic to L modulo N for every N > 0: in fact, there is a formula for the number of such lattices, called the Siegel mass formula. In this talk, I'll review the Siegel mass formula and how it can be deduced from a conjecture of Weil on volumes of adelic points of algebraic groups. This conjecture was proven for number fields by Kottwitz, building on earlier work of Langlands and Lai. I will conclude by sketching joint work (in progress) with Dennis Gaitsgory, which uses topological ideas to attack Weil's conjecture in the case of function fields.

In the Said Business School

The covariance between nominal bonds and stocks has varied considerably over recent decades and has even switched sign. It has been predominantly positive in periods such as the late 1970s and early 1980s when the economy has experienced supply shocks and the central bank has lacked credibility. It has been predominantly negative in periods such as the 2000s when investors have feared weak aggregate demand and deflation. This lecture discusses the implications of changing bond risk for the shape of the yield curve, the risk premia on bonds, and the relative pricing of nominal and inflation-indexed bonds.