Volume 170 Issue 1 – July 2009

## Bounds on Faltings’s delta function through covers

Pages 1-43 by Jay Jorgenson, Jürg Kramer

## The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible

Pages 45-65 by F. Thomas Farrell, Pedro Ontaneda

## Local rigidity of affine actions of higher rank groups and lattices

Pages 67-122 by David Fisher, Gregory Margulis

## Minimal co-volume hyperbolic lattices, I: The spherical points of a Kleinian group

Pages 123-161 by Frederick W. Gehring, Gaven J. Martin

## Singularities of the Prym theta divisor

Pages 163-204 by Sebastian Casalaina-Martin

## Inverse spectral problem for analytic domains, II: $\mathbb Z_2$-symmetric domains

Pages 205-269 by Steve Zelditch

## Lie theory for nilpotent $L_\infty$-algebras

Pages 271-301 by Ezra Getzler

## The Ten Martini Problem

Pages 303-342 by Artur Avila, Svetlana Jitomirskaya

## The rationality of Stark-Heegner points over genus fields of real quadratic fields

Pages 343-369 by Massimo Bertolini, Henri Darmon

## Additive approximation for edge-deletion problems

Pages 371-411 by Noga Alon, Asaf Shapira, Benny Sudakov

## Local connectivity of Julia sets for unicritical polynomials

Pages 413-426 by Jeremy Kahn, Mikhail Lyubich

## Fitting a $C^m$-smooth function to data, III

Pages 427-441 by Charles Fefferman

## Exponential growth and an asymptotic formula for the ranks of homotopy groups of a finite 1-connected complex

Pages 443-464 by Yves Felix, Steve Halperin, Jean-Claude Thomas

## Pólya-Schur master theorems for circular domains and their boundaries

Pages 465-492 by Julius Borcea, Petter Brändén

## Erratum to “The homotopy type of the matroid Grassmannian”

Pages 493-493 by Daniel K. Biss