The Rosetta Stone of L-functions -- New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography -- Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data -- Open Questions on the Mumford-Shah Functional -- Multi-scale Modeling -- Mass in Quantum Yang-Mills Theory (Comment on a Clay Millennium Problem) -- On Scaling Properties of Harmonic Measure -- The Heritage of Fourier -- The Quantum-Mechanical Many-Body Problem: The Bose Gas -- Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle -- Heat Measures and Unitarizing Measures for Berezinian Representations on the Space of Univalent Functions in the Unit Disk -- On Local and Global Existence and Uniqueness of Solutions of the 3D Navier—Stokes System on ?3 -- Analysis on Lie Groups: An Overview of Some Recent Developments and Future Prospects -- Encounters with Science: Dialogues in Five Parts.The purpose of the essays collected in this volume is to consider the future of analysis and related areas of physics. It is published in honor of Lennart Carleson, who has devoted much of his career to broadening the scope of harmonic analysis. Written by leading mathematicians and mathematical physicists, the articles should inspire new avenues of research. The collection shows the impressive relationship between physical intuition and mathematical analysis. These essays give confidence that the meeting ground between these areas of mathematics and physics will only grow more fertile in the future.