What is he best known for?
The fields of study he is best known for:
- Pure mathematics
- Algebra
- Representation theory
Brian Parshall focuses on Pure mathematics, Algebra, Affine Lie algebra, Group cohomology and Graded Lie algebra.
Pure mathematics is closely attributed to Discrete mathematics in his work.
Brian Parshall combines subjects such as Stratification and Quadratic algebra with his study of Algebra.
His Affine Lie algebra research includes themes of Non-associative algebra and Quantum group.
His study in the field of Factor system also crosses realms of Divisible group.
His studies deal with areas such as Modular representation theory and -module as well as Graded Lie algebra.
His most cited work include:
- Finite dimensional algebras and highest weight categories. (743 citations)
- Quantum linear groups (303 citations)
- Rational and Generic Cohomology (188 citations)
What are the main themes of his work throughout his whole career to date?
His primary areas of study are Pure mathematics, Algebra, Cohomology, Discrete mathematics and Algebraic group.
Borrowing concepts from Schur algebra, Brian Parshall weaves in ideas under Pure mathematics.
As part of one scientific family, Brian Parshall deals mainly with the area of Algebra, narrowing it down to issues related to the Affine Lie algebra, and often Non-associative algebra.
His study looks at the relationship between Cohomology and topics such as Reductive group, which overlap with Algebraic cycle.
His work carried out in the field of Discrete mathematics brings together such families of science as Group and Kazhdan–Lusztig polynomial.
The study incorporates disciplines such as Coxeter element and Algebraically closed field, Simply connected space, Combinatorics in addition to Algebraic group.
He most often published in these fields:
- Pure mathematics (65.35%)
- Algebra (35.43%)
- Cohomology (22.83%)
What were the highlights of his more recent work (between 2007-2018)?
- Pure mathematics (65.35%)
- Algebraic group (19.69%)
- Algebraic number (14.96%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Pure mathematics, Algebraic group, Algebraic number, Cohomology and Representation theory.
His Pure mathematics research is multidisciplinary, incorporating elements of Discrete mathematics and Structure.
Within one scientific family, Brian Parshall focuses on topics pertaining to Weyl group under Discrete mathematics, and may sometimes address concerns connected to Kazhdan–Lusztig polynomial.
His research in Algebraic number intersects with topics in Group of Lie type, Classification of finite simple groups, Root of unity and Quantum group.
His Cohomology research incorporates elements of Reductive group and Degree.
Representation theory is a primary field of his research addressed under Algebra.
Between 2007 and 2018, his most popular works were:
- Reduced standard modules and cohomology (44 citations)
- Bounding Ext for modules for algebraic groups, finite groups and quantum groups ✩ (29 citations)
- Cohomology for Quantum Groups Via the Geometry of the Nullcone (27 citations)
In his most recent research, the most cited papers focused on:
- Pure mathematics
- Representation theory
- Algebra
Brian Parshall mainly investigates Pure mathematics, Algebraic number, Algebraic group, Cohomology and Representation theory.
His Pure mathematics study frequently links to adjacent areas such as Structure.
His Algebraic group study combines topics from a wide range of disciplines, such as Discrete mathematics, Coxeter element and Simply connected space.
His Coxeter element research integrates issues from Quantum group and Lie algebra.
Cohomology is represented through his Group cohomology and Equivariant cohomology research.
His Étale cohomology study, which is part of a larger body of work in Group cohomology, is frequently linked to Galois cohomology, bridging the gap between disciplines.
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