“Algebraic Techniques in Geometry: The 10th Anniversary,” by Micha Sharir

02 Aug 2018 55:45 0
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“Algebraic Techniques in Geometry: The 10th Anniversary,” by Micha Sharir Clip Video - For the past 10 years, combinatorial geometry (and to some extent, computational geometry too) has gone through a dramatic revolution, due to the infusion of techniques from algebraic geometry and algebra that have proven effective in solving a variety of hard problems that were thought to be unreachable with more traditional techniques. The new era has begun with two groundbreaking papers of Guth and Katz, in 2008 and 2010. Their second paper has (almost completely) solved the notoriously hard distinct distances problem of Erdős, open since 1946.

It is now high time to celebrate the decade of extensive achievements that have been made since 2008, and in this talk I will survey some of the progress that has been made, including a variety of problems on distinct and repeated distances and other configurations, on incidences between points and lines, curves, and surfaces in two, three, and higher dimensions, on polynomials vanishing on Cartesian products with applications, on cycle elimination for lines and triangles in three dimensions, on range searching with semialgebraic sets, and I will most certainly run out of time while doing so.

https://dl.acm.org/citation.cfm?id=3209028


Tags: Algebraic Techniques, Geometry, ISSAC 2018, ACM ISSAC

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