The field of combinatorial geometry has some of its roots in profound questions asked by Paul Erdos, back in the 1940s. Erdos continued to investigate many aspects of the field, shaping it in the process, and helped make it a deep, rich, and intensively studied branch of mathematics. In the 1980s, computer scientists became involved due to applications to computational geometry, and in the 1990s, harmonic analysts became interested due to its relationship with the Kakeya problem.
In the past four years, the landscape of combinatorial geometry has considerably changed due to the work of Guth and Katz (inspired by earlier work of Dvir on the finite field Kakeya problem), who solved the joints problem in 3D and the Erdos distinct distances problem. More recently, Green and Tao stunningly solved the long-standing conjecture of Dirac and Motzkin on the number of ordinary lines. What these results have in common is algebraic geometry.
The application of algebraic geometry to problems in incidence geometry has been a rather surprising development. This interdisciplinary work is still at its infancy, and a major goal of this program is to provide a venue for deepening and widening the interaction between combinatorial geometry, algebraic geometry, Fourier analysis, and hopefully other mathematical disciplines too.
Jordan Ellenberg
(University of Wisconsin-Madison)
Nets Katz, Chair
(California Institute of Technology)
Micha Sharir
(Tel Aviv University)
Jozsef Solymosi
(University of British Columbia)
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