Algebra, Geometry, and Physics in the 21st Century : Kontsevich Festschrift

Description

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 Front Matter ....Pages i-vii Adiabatic Limits of Co-associative Kovalev–Lefschetz Fibrations (Simon Donaldson)....Pages 1-29 Ideal Webs, Moduli Spaces of Local Systems, and 3d Calabi–Yau Categories (A. B. Goncharov)....Pages 31-97 Spectral Sequences for Cyclic Homology (D. Kaledin)....Pages 99-129 Derived Varieties of Complexes and Kostant’s Theorem for \(\mathfrak{gl}(\mathrm{m}|\mathrm{n})\) (M. Kapranov, S. Pimenov)....Pages 131-176 Higher Symmetry and Gapped Phases of Gauge Theories (Anton Kapustin, Ryan Thorngren)....Pages 177-202 Constructing Buildings and Harmonic Maps (Ludmil Katzarkov, Alexander Noll, Pranav Pandit, Carlos Simpson)....Pages 203-260 Cohomological Hall Algebras, Semicanonical Bases and Donaldson–Thomas Invariants for 2-dimensional Calabi–Yau Categories (with an Appendix by Ben Davison) (Jie Ren, Yan Soibelman)....Pages 261-293 Fukaya A∞-structures Associated to Lefschetz Fibrations. II (Paul Seidel)....Pages 295-364