This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.

Inhalt
The Hirzebruch signature theorem for conical metrics.- Depth and the local Langlands correspondence.- Guide to elliptic boundary value problems for Dirac-type operators.- Symplectic and hyperkähler implosion.- Kazhdan-Lusztig conjectures and shadows of Hodge theory.- Uniform sup-norm bounds on average for cusp forms of higher weights.- Fivebranes and 4-manifolds.- Higgs bundles and characteristic classes.- Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces.- On Lusztig's q-analogues of all weight multiplicities of a representation.- The triangulation of manifolds: topology, gauge theory, and history.- Elliptic Calabi-Yau threefolds over a del Pezzo surface.- Remarks on cohomological Hall algebras and their representations.- A stratification on the moduli of K3 surfaces in positive characteristic.- The right adjoint of the parabolic induction.