Geometry and Topology

Formal Groups and ApplicationsAn 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.

 Read more


Algebra and Algebraic Geometry

Formality of the Little N-disks Operad
Pascal Lambrechts and Ismar Volić
In this paper, the authors develop the details of Kontsevich's proof of the formality of little N-disks operad over the field of real numbers. Read More

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. Read More

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. Read More

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). Read More

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". Read More

Analysis

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. Read More

Differential Equations

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. Read More

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. Read More

Local Analytic Classification of q-Difference Equations
Jean-Pierre Ramis, Jacques Sauloy, and Changgui Zhang
The authors essentially achieve Birkhoff's program for q-difference equations by giving three different descriptions of the moduli space of isoformal analytic classes. Read More

Geometry and Topology

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. Read More

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. Read More

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). Read More

Logic and Foundations

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. Read More

Mathematical Physics

Weyl Law for Semi-Classical Resonances with Randomly Perturbed Potentials
Johannes Sjöstrand
Read More

Effective Hamiltonians for Constrained Quantum Systems
Jakob Wachsmuth and Stefan Teufel
Read More