Continuity of the Alvarez class under deformations

A foliated manifold (M,F) is minimizable if there exists a Riemannian metric g on M such that every leaf of F is a minimal submanifold of (M,g). Alvarez Lopez defined a cohomology class of degree 1 called the Alvarez class of (M,F) whose triviality characterizes the minimizability of (M,F), when M is closed and F is Riemannian. In this paper, we show that the family of the Alvarez classes of a smooth family of Riemannian foliations is continuous with respect to the parameter. Since the Alvarez class has algebraic rigidity under certain topological conditions on (M,F) as the author showed in arXiv:0909.1125, we show that the minimizability of Riemannian foliations is invariant under deformation under the same topological conditions.Comment: 31 pages, 2 figures, to appear in J. Reine. Angew. Math.. Proposition 6 was added to correct a mistake in the paragraph after Question 5. Minor corrections on grammar have also been mad

Mugar Book Club, Summer 2018 (Launch)

Poster promoting the 2018 Mugar Book Club and announcing the first book to be discussed: "How the Garcia Girls Lost Their Accents" by Julia Alvarez

Region-wide temporal and spatial variation in Caribbean reef architecture: is coral cover the whole story?

The architectural complexity of coral reefs is largely generated by reef-building corals, yet the effects of current regional-scale declines in coral cover on reef complexity are poorly understood. In particular, both the extent to which declines in coral cover lead to declines in complexity and the length of time it takes for reefs to collapse following coral mortality are unknown. Here we assess the extent of temporal and spatial covariation between coral cover and reef architectural complexity using a Caribbean-wide dataset of temporally replicated estimates spanning four decades. Both coral cover and architectural complexity have declined rapidly over time, with little evidence of a time-lag. However, annual rates of change in coral cover and complexity do not covary, and levels of complexity vary greatly among reefs with similar coral cover. These findings suggest that the stressors influencing Caribbean reefs are sufficiently severe and widespread to produce similar regional-scale declines in coral cover and reef complexity, even though reef architectural complexity is not a direct function of coral cover at local scales. Given that architectural complexity is not a simple function of coral cover, it is important that conservation monitoring and restoration give due consideration to both architecture and coral cover. This will help ensure that the ecosystem services supported by architectural complexity, such as nutrient recycling, dissipation of wave energy, fish production and diversity, are maintained and enhanced

Same Day Voter Registration in North Carolina

R. Michael Alvarez of the California Institute of Technology and Jonathan Nagler of NYU analyze the likely impact of Election Day Registration on voter turnout in North Carolina

Election Day Voter Registration in Iowa

R. Michael Alvarez of the California Institute of Technology and Jonathan Nagler of NYU analyze the likely impact of Election Day Registration on voter turnout in Iowa

The 5-D Choptuik critical exponent and holography

Recently, a holographic argument was used to relate the saturation exponent, $\gamma_{BFKL}$, of four-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, $\gamma_{5d}$, in 5-dimensional black hole formation via scalar field collapse \cite{alvarez-gaume}. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of $\gamma_{5d}$ with substantially decreased numerical error. Our current result is $\gamma_{5d} = 0.4131 \pm 0.0001$, which is close to, but not in strict agreement with, the value of $\gamma_{BFKL}=0.409552$ quoted in \cite{alvarez-gaume}.Comment: 11 pagers, 2 figure

Too good to be true : asset pricing implications of pessimism

We evaluate whether the introduction of pessimistic homogeneous beliefs in the frictionless Lucas-Mehra-Prescott model and the Kehoe-Levine-Alvarez-Jermann model with endogenous bor- rowing constraints, helps explain the equity premium, the risk-free rate and the equity volatility puzzles as well as the short-term momentum and long-term reversal of excess returns. We cal- ibrate the model to U.S. data as in Alvarez and Jermann [4] and we find that the data does not contradict the qualitative predictions of the models. When the preferences parameters are disciplined to match both the average annual risk-free rate and equity premium, the Lucas-Mehra- Prescott model gives a more quantitatively accurate explanation for short-term momentum than the Kehoe-Levine-Alvarez-Jermann model but the latter gives a more quantitatively accurate ex- planation for the equity volatility puzzle. Long-term reversal remains quantitatively unexplained in both models

Election Day Voter Registration in Massachusetts

R. Michael Alvarez of the California Institute of Technology and Jonathan Nagler of NYU analyze the likely impact of Election Day Registration on voter turnout in Massachusetts

Matrix model with superconformal symmetry

A matrix model is presented which leads to the discrete ``eigenvalue model'' proposed recently by Alvarez-Gaum\'e {\it et.al.} for 2D supergravity (coupled to superconformal matters).Comment: 7p