What is he best known for?
The fields of study he is best known for:
- Pure mathematics
- Algebra
- Mathematical analysis
Dmitri Orlov mostly deals with Coherent sheaf, Pure mathematics, Derived category, Algebra and Derived algebraic geometry.
His work on Coherent sheaf is being expanded to include thematically relevant topics such as Projective test.
His study in Homological mirror symmetry and Triangulated category is carried out as part of his studies in Pure mathematics.
Many of his studies involve connections with topics such as Noncommutative geometry and Derived category.
He works on Algebra which deals in particular with Sheaf.
As part of one scientific family, he deals mainly with the area of Sheaf, narrowing it down to issues related to the Concrete category, and often Direct image with compact support, Closed category and Enriched category.
His most cited work include:
- TRIANGULATED CATEGORIES OF SINGULARITIES AND D-BRANES IN LANDAU-GINZBURG MODELS (489 citations)
- Equivalences of derived categories and K3 surfaces (421 citations)
- Semiorthogonal decompositions for algebraic varieties. (382 citations)
What are the main themes of his work throughout his whole career to date?
His scientific interests lie mostly in Pure mathematics, Coherent sheaf, Derived category, Algebra and Homological mirror symmetry.
His work focuses on many connections between Pure mathematics and other disciplines, such as Gravitational singularity, that overlap with his field of interest in Algebraic variety.
His Coherent sheaf research incorporates elements of Commutative property, Equivalence, Geometry, Bounded function and Abelian group.
His study explores the link between Derived category and topics such as Homotopy category that cross with problems in Adjoint functors.
In general Algebra, his work in Sheaf, Abelian category and Scheme is often linked to Derived algebraic geometry linking many areas of study.
His Mirror symmetry research includes themes of Cohomology and Brane cosmology.
He most often published in these fields:
- Pure mathematics (56.84%)
- Coherent sheaf (37.89%)
- Derived category (26.32%)
What were the highlights of his more recent work (between 2013-2020)?
- Pure mathematics (56.84%)
- Noncommutative geometry (15.79%)
- Type (9.47%)
In recent papers he was focusing on the following fields of study:
The scientist’s investigation covers issues in Pure mathematics, Noncommutative geometry, Type, Scheme and Vector bundle.
His biological study focuses on Projective test.
His study looks at the intersection of Type and topics like Coherent sheaf with Embedding.
The subject of his Scheme research is within the realm of Algebra.
The study incorporates disciplines such as Morphism, Differential and Line in addition to Algebra.
His work in Vector bundle covers topics such as Quiver which are related to areas like Discrete mathematics and Projective space.
Between 2013 and 2020, his most popular works were:
- SMOOTH AND PROPER NONCOMMUTATIVE SCHEMES AND GLUING OF DG CATEGORIES (79 citations)
- Geometric realizations of quiver algebras (32 citations)
- Gluing of categories and Krull-Schmidt partners (5 citations)
In his most recent research, the most cited papers focused on:
- Pure mathematics
- Mathematical analysis
- Algebra
His primary areas of study are Pure mathematics, Projective test, Subcategory, Noncommutative geometry and Scheme.
Dmitri Orlov combines subjects such as Function, Vector bundle, Quiver and Endomorphism with his study of Projective test.
His biological study spans a wide range of topics, including Characterization, Separable space, Differential and Generator.
His Noncommutative geometry study typically links adjacent topics like Coherent sheaf.
His Scheme study combines topics in areas such as Idempotence, Embedding, Global dimension and Differential graded category.
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