1 2 SABIN CAUTIS, JOEL KAMNITZER, AND ANTHONY LICATA This paper is part of the program laid out in [CK2] for categorifying Reshitikhin-Turaev tangle invariants using geometric representation theory. Let us brie?y recall the main idea explained in the introduction to that paper. LetGbe plex...
groupisfinite.ToprovethisandsomeotherfinitenessresultswefurtherdevelopEriksson’stheoryofageometricrepresentationofCoxetergroupsandobservesomecuriousdifferencesofthisrepresentationfromthestandardgeometricrepresentation.Keywords:numbersgame,generalizedCartanmatrix,Dynkindiagram,Coxetergraph,Coxeter/Weylgroup,geometric...
Mukkamala, P., Szegedy, M.: Geometric representation of cubic graphs with four directions. Comput. Geom. 42(9) (2009) 842-851Mukkamala, P., Szegedy, M.: Geometric representation of cubic graphs with four di- rections. Computational Geometry: Theory and Applications 42(9), 842-851 (2009...
GEOMETRICFUNCTIONTHEORYDAVIDBEN-ZVIDearCafePatrons,InthisguestpostIwanttobrieflydiscusscorrespondences,integraltransformsandtheircate-gorificationastheyapplytorepresentationtheory,atopicthatmightbecalledgeometricfunctiontheory.Thishasbeenoneofthefundamentalparadigmsofgeometricrepresentationtheory(to-getherwithlocalizationof...
In 1873, the English mathematician and philosopher William Clifford invented a deceptively simple algebraic system unifying Cartesian coordinates with complex numbers, and offering a compact representation of lines, areas and volumes, as well as rotations, in 3-space. In more advanced physics, Clifford...
et al. Automatic chemical design using a data-driven continuous representation of molecules. ACS Centr. Sci. 4, 268–276 (2018). Article Google Scholar O’Boyle, N. & Dalke, A. DeepSmiles: An adaptation of smiles for use in machine-learning of chemical structures. Preprint at https://...
I.M. James, in Handbook of Algebraic Topology, 1995 In Poincaré's work the discussion is mainly conducted in geometric terms. It was not until much later that the value of a more algebraic approach became recognized. By the thirties the terms “Algebraic Topology” and “Geometric Topology”...
Zhang et al. Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning. NeurIPS 2021 Chamberlain, Shirobokov, et al. Graph Neural Networks for Link Prediction with Subgraph Sketching. ICLR 2023 ...
howeveritdoesnotdependonthesmoothnessofthedata.TheHamilton-Jacobiequationsareclassicallyderivedfromthecalculusofvariations,andtheinterestoffindingviscositysolutions(notionintro-ducedbyM.G.Crandall-P.L.Lions[8])ofproblem(1.1)iswell-knowninoptimalcontrolanddifferentialgamestheory(c.f.M.Bardi-I.Capuzzo...
geometricinterpretationrepresentationtheoryalgebraicgroupsoverarbitraryrings.representationtheoreticsidecorrespondsperversesheaves,familiarfromuniversalcoefficientalgebraictopology.Notewefirstproveourresultp-adicintegers)positivecharacteristic).Wedoknowhowpositivecharacteristicdirectly.Onekeytechnicalpointscertainalgebraiccyclesturn...