The study of metric spaces with upper and lower sectional curvature bounds  is a rich and well developed subject that goes back some 60+ years to the work of A.D. Alexandrov.  It has a wide variety of applications and connections with various areas of geometry such as geometric group theory, classical Riemannian geometry of manifolds with various sectional curvature bounds, integral geometry and the study of spaces with lower Ricci bounds.

The planned workshop has two main aims:

*    To bring together experts to report on recent progress and to establish new goals and connections between various areas of the field.
*    To familiarize young mathematicians  and graduate  students with the basics of the theory as well as recent developments. To this end we are planning to have two mini-courses: one on spaces with lower curvature bounds and one on spaces with upper curvature bounds.

The lecture series will be meant to review both the basics of the theory as well as recent developments. They should be of interest to all levels of researchers from graduate students to postdocs to specialists in the field. We also plan to have standalone talks.  

A particular goal is to bring together and familiarize scientists with each other's research: people working on various aspects of the theory of spaces with upper and lower curvature bounds as well as people who work on somewhat outside but closely related topics. Such topics have proved spectacularly successful with an extremely wide variety of applications from small cancellation groups, to relatively and semi-hyperbolic groups, automatic groups, Teichmüller theory, mapping class groups, automorphisms of free groups, random groups and virtually fibered conjecture for 3 manifolds.

The workshop will also aim to address structure theory of $\mathrm{CAT}(K)$ spaces, Alexandrov spaces of positive and nonnegative curvature with low cohomogeneity, relations to submetries and Riemannian foliations, analysis on Alexandrov spaces (both with upper and lower curvature bounds), relations between Alexandrov and integral geometry and harmonic maps to and from spaces with various curvature bounds and lastly, upper and lower sectional curvature bounds for Lorentzian spaces.

Coveraged provided by ERC AdG RicciBounds, grant agreement 694405.

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