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[more ▼]We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space AdS3, which are defined as the intersection of the projective model of AdS3 with a convex polyhedron in RP3 whose vertices are all outside of AdS3 and whose edges all meet AdS3. We show that hyperideal polyhedra in AdS3 are uniquely determined by their combinatorics and dihedral angles, as well as by the induced metric on their boundary together with an additional combinatorial data, and describe the possible dihedral angles and the possible induced metrics on the boundary. [less ▲]Detailed reference viewed: 95 (3 UL) Polynomial quadratic differentials on the complex plane and light-like polygons in the Einstein UniverseTamburelli, Andrea in Advances in Mathematics (2019), 352We construct geometrically a homeomorphism between the moduli space of polynomial quadratic differentials on the complex plane and light-like polygons in the 2-dimensional Einstein Universe. As an ... [more ▼]We construct geometrically a homeomorphism between the moduli space of polynomial quadratic differentials on the complex plane and light-like polygons in the 2-dimensional Einstein Universe. As an application, we find a class of minimal Lagrangian maps between ideal polygons in the hyperbolic plane. [less ▲]Detailed reference viewed: 132 (6 UL) Differentials on graph complexesKhoroskhin, Anton; Willwacher, Thomas; Zivkovic, Marko in Advances in Mathematics (2017), 307We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains the graph cohomology. In ... [more ▼]We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains the graph cohomology. In particular, these spectral sequences may be used to show the existence of an infinite series of previously unknown and provably non-trivial cohomology classes, and put constraints on the structure of the graph cohomology as a whole. [less ▲]Detailed reference viewed: 176 (12 UL) Higher traces, noncommutative motives, and the categorified Chern characterScherotzke, Sarah ; Sibilla, Nicolo; Hoyois, Marcin Advances in Mathematics (2017)Detailed reference viewed: 31 (0 UL) Multiple edges in M. Kontsevich's graph complexes and computations of the dimensions and Euler characteristicsWillwacher, Thomas; Zivkovic, Marko in Advances in Mathematics (2015), 272We study the cohomology of complexes of ordinary (non- decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains the graph cohomology. In ... [more ▼]We study the cohomology of complexes of ordinary (non- decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains the graph cohomology. In particular, these spectral sequences may be used to show the existence of an infinite series of previously unknown and provably non-trivial cohomology classes, and put constraints on the structure of the graph cohomology as a whole. [less ▲]Detailed reference viewed: 140 (5 UL) Fourier-Mukai transform in the quantized settingPetit, François in Advances in Mathematics (2014), 256We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an ... [more ▼]We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an equivalence between the derived categories of coherent sheaves. [less ▲]Detailed reference viewed: 109 (5 UL) An analogue of Cobham's theorem for graph directed iterated function systemsCharlier, Emilie; Leroy, Julien ; Rigo, Michelin Advances in Mathematics (2014)Detailed reference viewed: 103 (3 UL) Classification of maximal transitive prolongations of super-Poincaré algebrasSanti, Andrea ; Altomani, Andrea in Advances in Mathematics (2014), (265), 60-96Detailed reference viewed: 105 (1 UL) Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applicationsNarayanan, E.K.; Pasquale, Angela; Pusti, Sanjoy in Advances in Mathematics (2014), 252A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\l$ is obtained for all $\l \in \fa^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\l$ away from the walls of a Weyl ... [more ▼]A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\l$ is obtained for all $\l \in \fa^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\l$ away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The $L^p$-theory for the hypergeometric Fourier transform is developed for \$0