Simon Donaldson facts for kids
Quick facts for kids
Simon Donaldson
FRS MAE
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Donaldson in 2009
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Simon Kirwan Donaldson
20 August 1957 Cambridge, England
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| Nationality | British |
| Alma mater | Pembroke College, Cambridge (BA) Worcester College, Oxford (DPhil) |
| Known for | Topology of smooth (differentiable) four-dimensional manifolds Donaldson theory Donaldson theorem Donaldson–Thomas theory Donaldson–Uhlenbeck–Yau theorem K-stability K-stability of Fano varieties Yau–Tian–Donaldson conjecture |
| Awards | Junior Whitehead Prize (1985) Fields Medal (1986) Royal Medal (1992) Crafoord Prize (1994) Pólya Prize (1999) King Faisal International Prize (2006) Nemmers Prize in Mathematics (2008) Shaw Prize in Mathematics (2009) Breakthrough Prize in Mathematics (2014) Oswald Veblen Prize (2019) Wolf Prize in Mathematics (2020) |
| Scientific career | |
| Fields | Topology |
| Institutions | Imperial College London Stony Brook University Institute for Advanced Study Stanford University University of Oxford |
| Thesis | The Yang–Mills Equations on Kähler Manifolds (1983) |
| Doctoral advisor | Michael Atiyah Nigel Hitchin |
| Doctoral students | Oscar Garcia Prada Dominic Joyce Dieter Kotschick Graham Nelson Paul Seidel Ivan Smith Gábor Székelyhidi Richard Thomas Michael Thaddeus |
Sir Simon Kirwan Donaldson (born on August 20, 1957) is a famous English mathematician. He is known for his important work on the topology of four-dimensional manifolds. These are like complex shapes or spaces. He also contributed to Kähler geometry, which is a special area of geometry.
Today, he is a permanent member at the Simons Center for Geometry and Physics in New York. He is also a Professor of Pure Mathematics at Imperial College London.
Contents
Simon Donaldson's Early Life and Education
Simon Donaldson's father was an electrical engineer. His mother also had a science degree. Both of his parents studied at the University of Cambridge.
Simon earned his first degree in mathematics from Pembroke College, Cambridge, in 1979. In 1980, he started his advanced studies at Worcester College, Oxford. He worked under the guidance of Nigel Hitchin and later Michael Atiyah.
A Big Discovery as a Student
While still a student, Simon Donaldson made a huge discovery in 1982. This discovery made him famous in the math world. He published his findings in a paper in 1983. His teacher, Michael Atiyah, said the paper "stunned the mathematical world."
Donaldson's work helped us understand four-dimensional shapes better. He used special math tools called "instantons." These tools come from a physics idea called gauge theory. His early work showed that many four-dimensional shapes cannot be "smooth." This means they don't have a perfectly even surface everywhere.
He also created new ways to measure these shapes. These measurements helped show that some four-dimensional shapes can have many different "smooth" versions. It was like finding "exotic" or unusual ways these shapes could exist.
After His Studies
After getting his PhD from Oxford University in 1983, Donaldson became a research fellow. He spent a year at the Institute for Advanced Study in Princeton, New Jersey. In 1985, he returned to Oxford University as a professor.
He later visited Stanford University for a year. In 1998, he moved to Imperial College London as a Professor of Pure Mathematics. In 2014, he joined the Simons Center for Geometry and Physics in New York.
Awards and Honors
Simon Donaldson has received many important awards for his work. He was invited to speak at the International Congress of Mathematicians (ICM) several times. He spoke in 1983, 1986, 1998, and 2018.
- In 1985, he received the Junior Whitehead Prize.
- In 1986, he was awarded the Fields Medal. This is one of the highest honors a mathematician can receive.
- In 1994, he won the Crafoord Prize in Mathematics.
- In 2006, he received the King Faisal International Prize for science. This was for his math theories that help us understand tiny particles.
- In 2008, he was awarded the Nemmers Prize in Mathematics.
- In 2009, he shared the Shaw Prize in Mathematics with Clifford Taubes. They were honored for their work on geometry in 3 and 4 dimensions.
- In 2014, he received the Breakthrough Prize in Mathematics. This award recognized his new ways of understanding 4-dimensional shapes.
- In 2019, he won the Oswald Veblen Prize in Geometry. He shared this with Xiuxiong Chen and Song Sun.
- In 2020, he received the Wolf Prize in Mathematics with Yakov Eliashberg.
He was made a Fellow of the Royal Society (FRS) in 1986. In 2012, he was knighted by the Queen for his services to mathematics. This means he can use the title "Sir." He also became a fellow of the American Mathematical Society in 2012.
He has also received honorary degrees from universities in France and Spain.
Simon Donaldson's Research
Simon Donaldson's research uses mathematical analysis to solve problems in geometry. He often works with gauge theory, 4-manifolds, and differential geometry. His work has led to several important ideas:
- He showed that if certain 4-dimensional shapes have a specific property, they can be broken down into simpler parts. This is sometimes called Donaldson's theorem.
- He found that some ways of connecting 4-dimensional shapes are not as simple as they are in higher dimensions.
- He proved that certain types of complex shapes have a special kind of measurement called a Hermitian–Einstein metric.
- He showed that a smooth algebraic surface can only be formed by joining two other 4-dimensional shapes if one of them has a specific negative property. This used his new "Donaldson invariant."
- He proved that any compact symplectic manifold can be described using a special kind of geometric tool called a Lefschetz pencil.
More recently, Donaldson has focused on a big problem in complex geometry. This problem connects "stability" conditions for shapes with the existence of "extremal" Kähler metrics. He made progress on this problem, especially for certain shapes called "toric" shapes.
In 2012, he solved a major part of this problem. He worked with Chen and Sun on the Kähler–Einstein metric case. This was a huge achievement that involved many complex papers.
Solving the Fano Manifolds Conjecture
In 2019, Simon Donaldson, along with Xiuxiong Chen and Song Sun, won the Oswald Veblen Prize in Geometry. They received this award for solving a long-standing math problem about Fano manifolds.
The problem stated that a Fano manifold has a special measurement (a Kähler–Einstein metric) if and only if it is "K-stable." This idea was first suggested in the 1980s by Shing-Tung Yau and later expanded by Gang Tian and Donaldson.
Their solution was published in a series of three articles in 2015. This was a major breakthrough in the field of geometry.
