2026 Michael H. Freedman: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	50	1064	907	495	394	175	13113

Michael H. Freedman publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Michael H. Freedman sits on this spectrum.

42 publications 537+

This scientist: 175 publications — 51st percentile

51% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Michael H. Freedman D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Michael H. Freedman sits on this spectrum.

30 D-Index 86+

This scientist: 50 D-Index — 71st percentile

71% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

2013 - Fellow of the American Mathematical Society
1994 - Fellow of John Simon Guggenheim Memorial Foundation
1987 - US President's National Medal of Science "For his proof of the Poincare Conjecture in dimension four: a toplogical four-manifold is homeomorphic to S4[4th power] it it is homotopy equivalent to S4 [4th power], one of the greatest achievemnets in mathematics in this century.", Presented by President Reagan at a White House Ceremony on June 25, 1987.
1986 - Fields Medal of International Mathematical Union (IMU) Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture.
1985 - Fellow of the American Academy of Arts and Sciences
1984 - Member of the National Academy of Sciences
1980 - Fellow of Alfred P. Sloan Foundation

Overview

Michael H. Freedman is affiliated with the University of California, Santa Barbara in the United States. Their research primarily spans the fields of Mathematics and Physics and Astronomy, with a strong concentration in subfields such as Geometry and Topology, Mathematical Physics, Artificial Intelligence, Astronomy and Astrophysics, and Nuclear and High Energy Physics.

The scientist's work covers several main topics, including:

Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Geometric Analysis and Curvature Flows
Black Holes and Theoretical Physics
Cosmology and Gravitation Theories
Quantum Computing Algorithms and Architecture
Topological and Geometric Data Analysis

Michael H. Freedman has published extensively, with a notable presence in venues such as arXiv (Cornell University), Journal of High Energy Physics, Advances in Mathematics, Nature, and Quantum. Some recent papers include:

"Curvature growth of some 4-dimensional gradient Ricci soliton singularity models," 2020, Advances in Mathematics
"Universality in long-distance geometry and quantum complexity," 2023, Nature
"Symmetry Protected Quantum Computation," 2021, Quantum
"The universe from a single particle," 2021, Journal of High Energy Physics
"The Group Structure of Quantum Cellular Automata," 2022, Communications in Mathematical Physics

Frequent collaborators in their research include Adam R. Brown, Modjtaba Shokrian Zini, Vyacheslav Krushkal, Matthew B. Hastings, and Michael Starbird.

The scientist has received numerous honors throughout their career, including:

Fellow of the American Mathematical Society (2013)
Fellow of John Simon Guggenheim Memorial Foundation (1994)
US President's National Medal of Science (1987) for their proof of the Poincaré Conjecture in dimension four
Fields Medal of International Mathematical Union (1986) for development of new methods in topological analysis of four-manifolds
Fellow of the American Academy of Arts and Sciences (1985)
Member of the National Academy of Sciences (1984)
Fellow of Alfred P. Sloan Foundation (1980)

Best Publications

The topology of four-dimensional manifolds

Michael Hartley Freedman

2330
Citations
Topology of 4-manifolds

Michael H. Freedman;Frank Quinn

979
Citations
Topologically protected qubits from a possible non-Abelian fractional quantum Hall state.

Sankar Das Sarma;Michael Freedman;Chetan Nayak;Chetan Nayak

896
Citations
Topological Quantum Computation

Michael H. Freedman;Alexei Kitaev;Alexei Kitaev;Michael J. Larsen;Zhenghan Wang

836
Citations
A Modular Functor Which is Universal for Quantum Computation

Michael H. Freedman;Michael Larsen;Zhenghan Wang

766
Citations
Interacting anyons in topological quantum liquids: The golden chain

Adrian Feiguin;Simon Trebst;Andreas W W Ludwig;Matthias Troyer

455
Citations
Mobius energy of knots and unknots

Michael H. Freedman;Zheng-Xu He;Zhenghan Wang

364
Citations
Simulation of Topological Field Theories¶by Quantum Computers

Michael H. Freedman;Alexei Kitaev;Zhenghan Wang

345
Citations
A class of P,T-invariant topological phases of interacting electrons

Michael Freedman;Chetan Nayak;Chetan Nayak;Kirill Shtengel;Kevin Walker

308
Citations
Bit threads and holographic entanglement

Michael Freedman;Matthew Headrick

307
Citations
Least area incompressible surfaces in 3-manifolds

Michael Freedman;Joel Hass;Peter Scott

292
Citations
The Two-Eigenvalue Problem and Density¶of Jones Representation of Braid Groups

Michael H. Freedman;Michael J. Larsen;Zhenghan Wang

273
Citations
P/NP, and the quantum field computer

Michael H. Freedman

260
Citations
Reflection positivity, rank connectivity, and homomorphism of graphs

Michael Freedman;László Lovász;Alexander Schrijver

259
Citations
Projective Plane and Planar Quantum Codes

Michael H. Freedman;David A. Meyer

208
Citations
Divergence-free fields : energy and asymptotic crossing number

Michael H. Freedman;Zheng-Xu He

191
Citations
Faster phase estimation

Krysta M. Svore;Matthew B. Hastings;Michael Freedman

155
Citations
Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state

Michael Freedman;Chetan Nayak;Chetan Nayak;Kevin Walker

151
Citations
4-Manifold topology I: Subexponential groups

Michael H. Freedman;Peter Teichner

125
Citations
A Magnetic Model with a Possible Chern-Simons Phase

Michael H. Freedman

108
Citations
Z(2)-Systolic Freedom and Quantum Codes

Michael H. Freedman;David A. Meyer;Feng Luo

105
Citations

Frequent Co-Authors

Chetan Nayak Microsoft (United States)

Krysta M. Svore Microsoft (United States)

László Lovász Eötvös Loránd University

Xiao-Liang Qi Stanford University

Matthias Troyer Microsoft (United States)

Charles Marcus University of Copenhagen

Martin Scharlemann University of California, Santa Barbara

Feng Luo Rutgers, The State University of New Jersey

Andreas W. W. Ludwig University of California, Santa Barbara

Alexander Schrijver University of Amsterdam

External Links

Wikipedia of Michael H. Freedman Personal website of Michael H. Freedman

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