2013 - Fellow of the American Mathematical Society
Pure mathematics, Derived category, Algebra, Cluster algebra and Triangulated category are his primary areas of study. Pure mathematics is frequently linked to Infinity in his study. His studies in Derived category integrate themes in fields like Homotopy category, Exact category and Homological algebra.
In the field of Algebra, his study on Differential graded category overlaps with subjects such as Differential. His study in Cluster algebra is interdisciplinary in nature, drawing from both Tilting theory and Quiver. His study looks at the relationship between Triangulated category and topics such as Category theory, which overlap with Stable module category, Grothendieck group, Lie algebra and Koszul duality.
His scientific interests lie mostly in Pure mathematics, Algebra, Cluster algebra, Derived category and Combinatorics. His research on Pure mathematics frequently links to adjacent areas such as Discrete mathematics. His Algebra research is multidisciplinary, relying on both Quadratic algebra and Algebra representation.
His Cluster algebra study combines topics in areas such as Conjecture, Representation theory, Categorification and Basis. The various areas that Bernhard Keller examines in his Derived category study include Abelian category, Homotopy, Cohomology, Bounded function and Homological algebra. As a part of the same scientific family, Bernhard Keller mostly works in the field of Combinatorics, focusing on Algebraic geometry and, on occasion, Number theory.
His primary areas of investigation include Pure mathematics, Cohomology, Differential, Functor and Algebra over a field. His research on Pure mathematics often connects related areas such as Cluster algebra. His Cluster algebra research is multidisciplinary, incorporating perspectives in Function, Perverse sheaf and Quiver.
The Cohomology study combines topics in areas such as Singularity, Koszul duality and Contractible space. Bernhard Keller interconnects Noetherian, Global dimension, Abelian category and Endomorphism ring in the investigation of issues within Derived category. His research integrates issues of Ring, Coherent ring, Noetherian scheme, Triangulated category and Abelian group in his study of Coherent sheaf.
Bernhard Keller focuses on Pure mathematics, Algebra over a field, Differential, Cohomology and Algebra. In most of his Pure mathematics studies, his work intersects topics such as Cluster algebra. His Algebra over a field research includes themes of Singularity and Isomorphism.
His work deals with themes such as Noncommutative geometry, Sheaf and Contractible space, Combinatorics, which intersect with Cohomology. He conducts interdisciplinary study in the fields of Algebra and Calculus through his works.
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On triangulated orbit categories.
Documenta Mathematica (2005)
Deriving DG categories
Annales Scientifiques De L Ecole Normale Superieure (1994)
On differential graded categories
Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures, Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 151-190 (2006)
Introduction to $A$-infinity algebras and modules
Homology, Homotopy and Applications (2001)
Chain complexes and stable categories.
Manuscripta Mathematica (1990)
Cluster-tilted algebras are Gorenstein and stably Calabi–Yau
Bernhard Keller;Idun Reiten.
Advances in Mathematics (2007)
Cluster algebras, quiver representations and triangulated categories
arXiv: Representation Theory (2010)
From triangulated categories to cluster algebras
Philippe Caldero;Bernhard Keller.
Inventiones Mathematicae (2008)
On the cyclic homology of exact categories
Journal of Pure and Applied Algebra (1999)
Derived Categories and Their Uses
Handbook of Algebra (1996)
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