Geometric higher groupoids and categories.- Hodge type theorems for arithmetic hyperbolic.- The Ding functional, Berndtsson convexity and moment maps.- Dimers and curvature formulae.- The norm of the Weierstrass Section.- Smooth family Thom-Smale complexes.- higher Analytic Torsion Polylogarithms and norm compatible elements on Abelian Schemes.- Teichmuller theory for conic surfaces.- On the analytic torsion of hyperbolic manifolds of the finite volume.- Log-correlated Gaussian elds: an overview.- A variation formula for the determinant line bundle. Compact subspaces of moduli spaces of stable bundles over class VII surfaces.- K-stability implies CM-stability.- Simple renormalization flow for FK-Percolation models.- Analytic torsion for BORCEA-VOISIN threefolds.