What is he best known for?
The fields of study he is best known for:
- Topology
- Pure mathematics
- Mathematical analysis
His primary areas of study are Pure mathematics, Combinatorics, Homology, Mathematical analysis and Torus.
His Pure mathematics study frequently draws connections to adjacent fields such as Discrete mathematics.
He interconnects Fixed point and Polynomial, Matrix polynomial in the investigation of issues within Combinatorics.
His studies deal with areas such as Riemann manifold, Geodesic and Symbolic dynamics as well as Homology.
His work carried out in the field of Torus brings together such families of science as Annulus, Homeomorphism and Boundary.
His Periodic point study combines topics from a wide range of disciplines, such as Manifold, Tangent bundle, Stable manifold, Hyperbolic set and Bounded function.
His most cited work include:
- HTTP Authentication: Basic and Digest Access Authentication (673 citations)
- Necessary conditions for stability of diffeomorphisms (212 citations)
- Geodesics on S2 and periodic points of annulus homeomorphisms (202 citations)
What are the main themes of his work throughout his whole career to date?
His main research concerns Pure mathematics, Combinatorics, Discrete mathematics, Fixed point and Mathematical analysis.
In his research, he undertakes multidisciplinary study on Pure mathematics and Morse code.
He combines subjects such as Image, Surface and Group, Group action with his study of Combinatorics.
The Discrete mathematics study combines topics in areas such as Equivalence and Stable manifold.
His study focuses on the intersection of Fixed point and fields such as Homeomorphism with connections in the field of Boundary and Annulus.
His work in Mathematical analysis tackles topics such as Homology which are related to areas like Rotation matrix and Symbolic dynamics.
He most often published in these fields:
- Pure mathematics (51.33%)
- Combinatorics (21.24%)
- Discrete mathematics (14.16%)
What were the highlights of his more recent work (between 2007-2020)?
- Pure mathematics (51.33%)
- Combinatorics (21.24%)
- Discrete mathematics (14.16%)
In recent papers he was focusing on the following fields of study:
John Franks mainly focuses on Pure mathematics, Combinatorics, Discrete mathematics, Mapping class group and Automorphism.
His Pure mathematics study frequently draws parallels with other fields, such as Fixed point.
His work deals with themes such as Elementary proof, Fixed-point theorem, Diffeomorphism and Orientation, which intersect with Fixed point.
His Combinatorics research is multidisciplinary, incorporating elements of Surface and Symplectic geometry.
John Franks works mostly in the field of Mapping class group, limiting it down to topics relating to Permutation group and, in certain cases, Projective geometry, Algebraic geometry, Hyperbolic geometry, Differential geometry and Finite set.
His Automorphism research includes elements of Embedding, Countable set and Nilpotent.
Between 2007 and 2020, his most popular works were:
- Groups of Homeomorphisms of One-Manifolds, I: Actions of Nonlinear Groups (25 citations)
- Global fixed points for centralizers and Morita's Theorem (15 citations)
- Cantor's Other Proofs that R Is Uncountable (14 citations)
In his most recent research, the most cited papers focused on:
- Topology
- Geometry
- Pure mathematics
The scientist’s investigation covers issues in Pure mathematics, Discrete mathematics, Mapping class group, Entropy and Automorphism.
Many of his studies involve connections with topics such as Perspective and Pure mathematics.
The study incorporates disciplines such as Mathematical proof and Arithmetic in addition to Discrete mathematics.
His Mapping class group study incorporates themes from Structured program theorem, Cohomology, Bounded function, Rotation number and Diffeomorphism.
His Entropy studies intersect with other disciplines such as Low complexity, Embedding, Countable set, Automorphism group and Nilpotent.
His study in Automorphism is interdisciplinary in nature, drawing from both Zero, Shift space and Linear subspace.
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