John Morgan (mathematician)

John Willard Morgan II (born April 28, 1946) is an American mathematician specializing in topology, particularly geometric topology and differential topology. He is a professor emeritus at Columbia University.

Morgan received his Ph.D. from Rice University in 1969, under the supervision of Michael Freedman. His research focuses on the classification of 3-manifolds and 4-manifolds, as well as related areas such as gauge theory and algebraic topology. He has made significant contributions to the understanding of the topology of manifolds and the development of new techniques for studying them.

Key areas of Morgan's work include:

• 3-Manifolds: Morgan has contributed significantly to the study of 3-manifolds, including work on the geometrization conjecture (Perelman's theorem) and the classification of 3-manifolds.

• 4-Manifolds: His research on 4-manifolds has involved Donaldson theory and its applications to understanding the topology of smooth 4-manifolds.

• Gauge Theory: Morgan has applied gauge theory, particularly Yang-Mills theory, to study the topology of manifolds.

• Ricci Flow: He has played a key role in understanding and popularizing Grigori Perelman's proof of the Poincaré conjecture and the geometrization conjecture, including co-authoring a book explaining Perelman's work.

Morgan has received numerous awards and honors for his contributions to mathematics. He is a member of the National Academy of Sciences. His work has had a profound impact on the field of topology and has influenced generations of mathematicians. He is widely regarded as a leading figure in modern topology.

Selected Publications:

• The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds (with Robert Friedman)
• Geometric Topology and Its Applications
• Perelman's Ricci Flow and the Poincaré Conjecture (with Gang Tian)