Lesley Sibner facts for kids

Lesley Millman Sibner (born August 13, 1934 – died September 11, 2013) was an American mathematician. She was also a professor of mathematics at the Polytechnic Institute of New York University.

Lesley earned her first degree in Mathematics from City College CUNY. She then completed her advanced degree, called a doctorate, at Courant Institute NYU in 1964. Her main teachers were Lipman Bers and Cathleen Synge Morawetz. Her special project, called a thesis, was about a type of math problem known as partial differential equations.

Exploring Math: Lesley Sibner's Research Career

In 1964, Lesley Sibner started teaching at Stanford University for two years. After that, she became a Fulbright Scholar in Paris. This scholarship allowed her to study at the Institut Henri Poincaré.

Working with Flows and Geometry

During this time, Lesley worked on her own projects. These included studying the Tricomi equation and how compressible flows behave. She also started working with her husband, Robert Sibner. Their work was inspired by a question from her teacher, Lipman Bers. They wanted to know if certain types of flows could exist on a Riemann surface.

To answer this, Lesley studied differential geometry and Hodge theory. These are advanced areas of math that deal with shapes and spaces. She and Robert proved an important math rule called a nonlinear Hodge–DeRham theorem. This rule was based on how one-dimensional harmonic forms act on closed shapes. They continued to work together on similar problems for many years.

Joining the Faculty and New Discoveries

In 1967, Lesley joined the faculty at Polytechnic University in Brooklyn, New York. In 1969, she proved the Morse index theorem. This was a big step in understanding certain math problems. She did this by making an older math idea, called Sturm–Liouville theory, even better.

From 1971 to 1972, she spent a year at the Institute for Advanced Study. There, she met famous mathematicians like Michael Atiyah and Raoul Bott. She realized her math skills could help solve problems in geometry. These problems were connected to the Atiyah–Bott fixed-point theorem. In 1974, Lesley and Robert Sibner found a new way to prove the Riemann–Roch theorem.

Exploring New Math Fields

Another mathematician, Karen Uhlenbeck, suggested Lesley work on the Yang-Mills equation. So, from 1979 to 1980, Lesley visited Harvard University. There, she learned about gauge field theory from Clifford Taubes. This led to new discoveries about special points, called point singularities, in the Yang-Mills equations.

Lesley became very interested in these singularities. This led her deeper into geometry. She worked with Robert Sibner to classify different types of singular connections. They also found a way to remove two-dimensional singularities.

In 1989, the Sibners and Karen Uhlenbeck worked together. They found that certain math objects, called instantons, could sometimes be seen as monopoles. They built non-minimal unstable critical points of the Yang-Mills functional. Lesley was asked to share this work at the Geometry Festival. In 1991, she was a Bunting Scholar at the Radcliffe Institute for Advanced Study.

For many years after, Lesley Sibner focused on gauge theory and gravitational instantons. Even though her research sounds like physics, she used ideas from physics to prove important math rules. These rules were about geometry and shapes.

In 2012, she became a fellow of the American Mathematical Society. This is a special honor for mathematicians.

See also

In Spanish: Lesley Sibner para niños