Algebraic geometryAlgebraic geometry -- Cycles and subschemes -- Riemann-Roch theoremsArithmetic rings and other special ringsCategory theory; homological algebraCategory theory; homological algebra -- Instructional exposition (textbooks, tutorial papers, etc.).Cluster algebrasCommutative algebraCommutative algebra -- Arithmetic rings and other special rings -- Cluster algebrasCommutative algebra -- Homological methods -- Local cohomologyCongressesCycles and subschemesDynamical systems and ergodic theoryDynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Rotation numbers and vectorsFree probability and free operator algebrasFunctional analysisFunctional analysis -- Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) -- Infinite-dimensional holomorphyFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Free probability and free operator algebrasFunctional analysis -- Topological algebras, normed rings and algebras, Banach algebras -- General theory of topological algebrasGeneral theory of topological algebrasGroup theory and generalizationsGroup theory and generalizations -- Representation theory of groups -- Representations of infinite symmetric groupsHomological methodsInfinite-dimensional holomorphyInstructional exposition (textbooks, tutorial papers, etc.)Local cohomology
