Geometry at Infinity

Part I. Large-scale geometry and asymptotic invariants.- Chapter 1. Large-scale geometry and asymptotic invariants.- Chapter 2. On the asymptotic equidistribution of word values in symmetric groups.- Chapter 3. Geometric invariants of local and arithmetic solvable groups.- Chapter 4. Infinite groups from the profinite point of view.- Chapter 5. Graphs at infinity: Liouville theorems, recurrence and characterization of Dirichlet Forms.- Chapter 6. Transgressing the algebraic coarse character map.- Chapter 7. Duality pairings with the analytic structure group.- Chapter 8. L2-invariants and Thurston’s vision.- Chapter 9. An invitation to fine curve graphs.- Chapter 10. Similarities between Euclidean Buildings and Riemannian Symmetric Spaces of Non-Compact Type.- Chapter 11. The geometry of branched covers of hyperbolic manifolds.- Part II. Moduli spaces and geometric structures.- Chapter 12. Axiom A flows and dynamical resonances for Anosov representations.- Chapter 13. Rigidity, deformations and limits of maximal representations.- Chapter 14. Asymptotic geometry of the Higgs bundle moduli space.- Chapter 15. Variations of stability and hyper-Kähler structures on moduli of parabolic Higgs Bundles.- Chapter 16. Self-duality solutions near infinity.- Chapter 17. Hypercomplex analytic spaces and schemes.- Chapter 18. Twistor geometric aspects of projective surfaces.- Part III. Curvature and topology.- Chapter 19. Spaces and Moduli Spaces of Metrics with Lower Curvature Bounds.- Chapter 20. The space of psc-concordances.- Chapter 21. Callias operators and quantitative metric inequalities with scalar curvature.- Chapter 22. Highly connected 7-manifolds, the linking form and non-negative curvature.- Chapter 23. Topology of Alexandrov Spaces with Cohomogeneity One Actions.- Chapter 24. Singular Riemannian foliations and collapse.- Chapter 25. Ricci flow and the scalar curvature rigidity of Einstein manifolds.- Chapter 26. Einstein metrics, their moduli spaces and stability.- Part IV. Geometric analysis and relativity.- Chapter 27. Synthetic notions of Ricci flow for metric measure spaces.- Chapter 28. Minimal surfaces in metric spaces.- Chapter 29. Nonunique tangent maps at isolated singularities of minimizing p-harmonic maps.- Chapter 30. Flowing Shapes: Theory and some Trends in the volume preserving Mean Curvature Flow and the Willmore Functional.- Chapter 31. Noncompact mean curvature flows.- Chapter 32. Evolution Equations on Manifolds with Conical Singularities.- Chapter 33. Solutions to Ricci flow whose scalar curvature is in Lp.- Chapter 34. Capillary hypersurfaces: Minkowski formulas, geometric inequalities and capillary Gauss curvature flow.- Chapter 35. A hitchhiker’s guide to first-order elliptic boundary value problems.- Chapter 36. Analysis on fibred cusp spaces.- Chapter 37. Some aspects of the spectral theory with twisting representations.- Chapter 38. Heat kernel asymptotics for quaternionic contact manifolds.- Chapter 39. On the construction of non time-symmetric initial data sets.- Chapter 40. Geometrically defined asymptotic coordinates in General Relativity.- Chapter 41. Homogeneous spacetimes inspired from Margulis spacetimes.