Peter B. Kronheimer facts for kids

Peter Benedict Kronheimer (born in 1963) is a British mathematician. He is famous for his work on how shapes and spaces work, especially in four dimensions. He uses a special area of math called gauge theory to study these shapes.

Today, he is a professor of mathematics at Harvard University. He also used to be the head of the math department there.

His School Days

Peter Kronheimer went to the City of London School when he was younger. Later, he studied at Oxford University. He earned his highest degree, a Doctor of Philosophy (DPhil), there. His main teacher and guide was a very famous mathematician named Michael Atiyah.

Peter Kronheimer has a long history with Merton College at Oxford. It is one of the oldest colleges at the university. He was a student there, both for his first degree and his advanced studies. He also became a full member of the college staff.

His Work and Discoveries

Peter Kronheimer's early work looked at special kinds of four-dimensional shapes. These shapes are important in understanding how space and gravity might work. He found ways to describe and classify these complex shapes.

He often worked with another mathematician, Tomasz Mrowka, from the Massachusetts Institute of Technology. They started working together at a math research center in Germany. Their first projects involved studying four-dimensional shapes that had a special surface inside them.

Solving Big Math Puzzles

Kronheimer and Mrowka used new mathematical tools to solve a long-standing puzzle. This puzzle was about how complicated a certain type of knot, called a torus knot, could be. They proved a theory by John Milnor about these knots.

They continued to develop their special math tools. They used these tools to understand more about how shapes behave in four dimensions.

One of their biggest achievements was proving the Thom conjecture. This was a very old and difficult problem in mathematics. It had puzzled mathematicians for many decades. Their work helped us understand more about how surfaces can be placed inside four-dimensional spaces.

They also proved another important idea called the Property P conjecture for knots. This helped mathematicians understand more about different types of knots. They even created a new way to study knots, which helped them prove that a special kind of math (Khovanov homology) can tell if a knot is just a simple loop or something more complex.

Books and Recognition

Besides his many research papers, Peter Kronheimer has written important books. He wrote one book about four-dimensional shapes with Simon Donaldson. He also wrote a book with Tomasz Mrowka called "Monopoles and Three-Manifolds." This book won the Doob Prize in 2011, which is a big award in mathematics.

Peter Kronheimer has been invited to speak at major international math conferences. He spoke at the International Congress of Mathematicians in Japan in 1990. In 2018, he gave a main speech at the same conference in Brazil, together with Tomasz Mrowka. In 2023, he received the Leroy P. Steele Prize for his important contributions to research.

His Students

Peter Kronheimer has guided many students who went on to become mathematicians themselves. Some of his PhD students include Ian Dowker, Jacob Rasmussen, Ciprian Manolescu, Olga Plamenevskaya, and Aliakbar Daemi.