## Contents of Volume 53, Number 1

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- Reciprocity laws and Galois representations: recent breakthroughs
- Jared Weinstein PDF
- Bull. Amer. Math. Soc.
**53**(2016), 1-39

- From rational billiards to dynamics on moduli spaces
- Alex Wright PDF
- Bull. Amer. Math. Soc.
**53**(2016), 41-56

- The nonlinear Schrödinger equation on tori: Integrating harmonic analysis, geometry, and probability
- Andrea R. Nahmod PDF
- Bull. Amer. Math. Soc.
**53**(2016), 57-91

- String theory and math: Why this marriage may last.
*Mathematics and dualities of quantum physics* - Mina Aganagic PDF
- Bull. Amer. Math. Soc.
**53**(2016), 93-115

## Mathematical Perspectives

- About the cover: Gauss and the
*Disquisitiones Arithmeticæ* - Gerald L. Alexanderson and Leonard F. Klosinski PDF
- Bull. Amer. Math. Soc.
**53**(2016), 117-120

- Selections Reprinted from
*Mathematical Reviews* - Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 121-142

##
Book Reviews

Book reviews do not contain an abstract. You may
download each review in this issue using the links
below.

- Methods of geometric analysis in extension and trace problems. Volume 1, by Alexander Brudnyi and Yuri Brudnyi.
- Methods of geometric analysis in extension and trace problems. Volume 2, by Alexander Brudnyi and Yuri Brudnyi.
- Reviewer: Garving K. Luli

- Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 143-149

- Control of nonholonomic systems: from sub-Riemannian geometry to motion planning, by Frédéric Jean.
- Reviewer: I. Zelenko

- Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 151-158

- Dense sphere packings: a blueprint for formal proofs, by Thomas C. Hales.
- Reviewer: Jeffrey C. Lagarias

- Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 159-166

- Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory, by Francesco Maggi.
- Reviewer: Alex Iosevich

- Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 167-171

- Upper and lower bounds for stochastic processes, by M. Talagrand.
- Reviewer: Antonio Auffinger

- Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 173-177

- Numerically solving polynomial systems with Bertini, by Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese and Charles W. Wampler.
- Reviewer: Henry Schenck

- Review information PDF
- Bull. Amer. Math. Soc.
**53**(2016), 179-186