Workshop I: Combinatorial Geometry Problems at the Algebraic Interface

Part of the Long Program Algebraic Techniques for Combinatorial and Computational Geometry
March 24 - 28, 2014

Overview

A major goal of the program is to study the development and applications of tools from algebraic geometry for the solution of problems in combinatorial (and computational) geometry, with incidence geometry as one focus. The goal of this workshop is to provide an arena for presenting and discussing research problems in incidence geometry and other related topics in combinatorial and computational geometry that seem amenable to the developed tools, including possible partial or full solutions to these problems.

Among the main themes that the workshop will cover are:

  • Incidence geometry: Incidences between points and lines in higher dimensions, incidences with other types of curves (such as circles), incidences with higher-dimensional surfaces.
  • Incidence-related problems: Repeated distances, distinct distances, congruent and similar simplices, unit-area triangles and unit-volume simplices, and other types of repeated patterns.
  • Combinatorial geometry at large: Geometric partitions, range searching, spanning trees with small crossing numbers, and relations between the new algebraic machinery and older sampling-based techniques.

Another goal of the workshop is to enhance and foster a two-way interaction between algebraic geometers and combinatorial and computational geometers, so as (a) to allow the latter community to learn more from algebraic geometers about the known tools and techniques that are relevant to combinatorial geometry, and (b) to attract algebraic geometers to the new application area, and get them involved in the study of the numerous challenging problems in algebraic geometry that the new area raises. We expect to achieve this goal by offering several survey talks on algebraic geometry, specially tailored problem sessions, and ample time for free discussions.

This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.

Organizing Committee

Haim Kaplan (Tel Aviv University)
Jiri Matousek (Charles University, Prague)
Micha Sharir (Tel Aviv University)
Terence Tao (University of California, Los Angeles (UCLA))