Algebraic techniques are playing an increasingly important role in certain areas of discrete geometry and combinatorics. This workshop will focus on those aspects of algebraic geometry that have an impact on incidence geometry and related areas. The workshop will primarily focus on those topics from classical algebraic geometry that seem poised to play important roles in this area including: the theory of ruled surfaces; Hilbert functions and polynomials; generalized Bezout theorems; the relationship between algebraic geometry over the field of real and complex numbers as well as fields of positive characteristic, combinatorial and algorithmic aspects of space decomposition induced by real algebraic varieties; and a variety of quantitative and combinatorial results in algebraic geometry.
A central challenge that the workshop will address is how to adequately identify the class of problems in discrete geometry susceptible to the algebraic method. The workshop will include expository talks by experts that make classical results of algebraic geometry accessible to researchers in discrete geometry by explaining them in modern terms. Another important goal of this workshop is to expose experts in algebraic geometry to new applications, and present them with some open problems.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
Igor Dolgachev (University of Michigan)
Jordan Ellenberg (University of Wisconsin-Madison)
Joseph Landsberg (Clay Scholar) (Texas A&M University - College Station)
Marie-Francoise Roy (Université de Rennes I)
Micha Sharir (Tel Aviv University)