Geometry and Topology

**An Introduction to Extremal Kähler Metrics**

**Gábor Székelyhidi, ***University of Notre Dame, IN*

This book gives an introduction to the study of extremal Kähler metrics, accessible to graduate students. The main focus is the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry.

**Formality of the Little N-disks Operad**

In this paper, the authors develop the details of Kontsevich's proof of the formality of little

**Tropical and Idempotent Mathematics and Applications**

Edited by: **G. L. Litvinov** and **S. N. Sergeev**

This volume contains articles on algebraic foundations of tropical mathematics as well as articles on applications of tropical mathematics in various fields as diverse as economics, electroenergetic networks, chemical reactions, representation theory, and foundations of classical thermodynamics.

**The Formal Theory of Tannaka Duality**

**Daniel Schäppi**

The author provides a list of sufficient conditions which ensure that an additive tensor category is equivalent to the category of representations of an affine groupoid scheme acting on an affine scheme, or, more generally, to the category of representations of a Hopf algebroid in a symmetric monoidal category.

**Introduction to the Theory of Standard Monomials: Second Edition **

**C. S. Seshadri**

The aim of this book is to give an introduction to what has come to be known as Standard Monomial Theory (SMT).

**Résumés des Cours au Collège de France: 1973–2000 **

**Jacques Tits**

The present volume reproduces the summaries of Jacques Tits' lectures, taken from the "Annuaires du Collége de France".

**Cocycles Over Partially Hyperbolic Maps**

**Artur Avila**, **Jimmy Santamaria**, **Marcelo Viana**, and **Amie Wilkinson**

The works collected in this volume, while addressing quite different goals, are focused on the same type of mathematical object: cocycles over partially hyperbolic diffeomorphisms.

**Microlocal Properties of Sheaves and Complex WKB**

**Alexander Getmanenko** and **Dmitry Tamarkin**

Kashiwara-Schapira style sheaf theory is used to justify analytic continuability of solutions of the Laplace transformed Schrödinger equation with a small parameter.

**Mathematics of Continuous and Discrete Dynamical Systems**

Edited by: **Abba B. Gumel**

This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9–10, 2013, in San Diego, CA.

**Local Analytic Classification of q-Difference Equations**

The authors essentially achieve Birkhoff's program for

**An Alpine Expedition through Algebraic Topology**

Edited by: **Christian Ausoni**, **Kathryn Hess**, **Brenda Johnson**, **Wolfgang Lück**, and **Jérôme Scherer**

The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic *K*-theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.

**Combinatorial Floer Homology**

**Vin de Silva**, **Joel W. Robbin**, and **Dietmar A. Salamon**

The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology.

**A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane**

**Fabian Ziltener**

Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold (*M*, ω).

**Generalized Descriptive Set Theory and Classification Theory**

**Sy-David Friedman**, **Tapani Hyttinen**, and **Vadim Kulikov**

In this paper the authors study the generalization where countable is replaced by uncountable.

**Weyl Law for Semi-Classical Resonances with Randomly Perturbed Potentials**

**Johannes Sjöstrand**

**Effective Hamiltonians for Constrained Quantum Systems**

**Jakob Wachsmuth** and **Stefan Teufel**