What Can We Make Out of Lines and Circles?

In 1880, French mathematician Jean Gaston Darboux started a project enumerating the various surfaces that can be made using grids of lines, circles or cross-sections of cones. Many examples of these surfaces appear in art and architecture. Mathematicians today have a complete list of the possible surfaces.

In this lecture, János Kollár will discuss how those ideas can be extended to higher dimensions, leading to fruitful questions about algebraic varieties with connections to number theory and symplectic geometry.

Kollár’s main interest is algebraic geometry, especially the moduli spaces of varieties, rationally connected varieties and the minimal model program. He also likes to explore related topics in algebra, complex analysis, differential geometry and computer science. He is a professor of mathematics at Princeton University and a member of the Hungarian Academy of Sciences, the National Academy of Sciences, the American Academy of Arts and Sciences. He was previously chair of the program committee of the 2018 International Congress of Mathematicians in Rio de Janeiro. He received the Cole Prize in 2006, the Nemmers Prize in 2016 and the Shaw Prize in 2017.