Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim's vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim's heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim's vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim's heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics.

The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.

Lively and engaging articles from the lectures and the participants of the 21st Goekova Geometry- Topology Conference, held on the shores of Goekova Bay, Turkey, in May of 2014.

This volume presents lively and engaging articles from the lecturers and the participants of the 25th and 26th Goekova Geometry-Topology Conferences, held on the shores of Goekova Bay, Turkey, in May/June of 2018 and May/June of 2019. The 25th and 26th Goekova Geometry-Topology Conferences were sponsored by the National Science Foundation, by the Turkish Mathematical Society, and by the European Research Council.

This volume presents lively and engaging articles from the lecturers and the participants of the 23rd Goekova Geometry-Topology Conference, held on the shores of Goekova Bay, Turkey, in May/June of 2016. Topics include manifolds, special holonomy, symplectic topology, gauge theory, Lie groups, hyperkahler manifolds, and more. The 23rd Goekova Geometry-Topology Conference was sponsored by the National Science Foundation, by the Turkish Mathematical Society, and by the European Research Council.

This volume presents lively and engaging articles from the lecturers and the participants of the 22nd Goekova Geometry-Topology Conference, held on the shores of Goekova Bay, Turkey, in May of 2015. Topics include high-dimensional geometric, symplectic and contact geometry, and more. The 22nd Goekova Geometry-Topology Conference was sponsored by the National Science Foundation, by the Turkish Mathematical Society, and by the European Research Council.

Lively and engaging articles from the lecturers and the participants of the 19th Goekova Geometry-Topology Conference, held on the shores of Goekova Bay, Turkey, in May of 2012.

The Goekova Geometry-Topology Conferences were inaugurated in 1992 with the support of TUBITAK (The Scientific and Technological Research Council of Turkey) and are held annually on the shores of the scenic Goekova Bay on the southwestern coast of Turkey. These conferences have been supported by TUBITAK since their inception and since 2005 they have received partial funding from NSF. Over the years the topics of these conferences were chosen from the exciting subjects of geometry and topology, usually with the most recent developments taking the front stage.

Lively and engaging articles from the lecturers and the participants of the 18th Goekova Geometry-Topology Conference, held on the shores of Goekova Bay, Turkey, in May of 2011.