Algebraic perspectives on space

Ezra Getzler is a professor at Northwestern University, Illinois, USA. Thanks to a grant from Knut and Alice Wallenberg Foundation, he will be a visiting professor at the the Department of Mathematics, Uppsala University.

Ezra Getzler, has received international recognition for his ground-breaking work in the fields of algebraic geometry and algebraic topology, often with close links to mathematical physics. He specialises in algebraic aspects of geometry. 

In many cases, algebra and geometry can be regarded as two sides of the same coin. Geometry is the study of spaces – their symmetries and transformations. One example of a transformation is a function that assigns a value to each point in space, such as a function that gives the temperature for each point in space. Such functions can be multiplied and added together, so they form an algebra. This algebra can then be explored using other mathematical methods, ultimately providing additional perspectives on the geometry of the original space. 

In the planned project, Ezra Getzler will work with specific spaces, called operads, where the space itself has an algebraic structure. One such geometric operad that Getzler will study is the Batalin-Vilkovisky operad. This type of operad also has important applications in mathematical physics’ quantum field theory and, in particular, it is a key ingredient in the string theory of modern theoretical physics.