MATH Seminar
| Title: Lines, Incidences, and a Conjecture of Solymosi |
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| Seminar: Combinatorics |
| Speaker: Albert Bush of Georgia Tech |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2012-04-06 at 4:00PM |
| Venue: W306 |
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| Abstract: Given any n points in the plane, the celebrated Szemeredi-Trotter theorem gives bounds on the number of lines that can each hit at least k points. J. Solymosi conjectured a significantly tighter bound with the stronger condition that the points be a grid and the lines be in general position -- no parallel lines, and no three lines meet at a single point. Using methods of Elekes as well as Borenstein and Croot, we prove Solymosi's conjecture. This is joint work with Gagik Amirkhanyan, Ernie Croot, and Chris Pryby. |
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