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Simons Center Special Colloquium: Points, Lines and Ranks of Design Matrices
Start Date: 2/13/2013Start Time: 2:00 PM
End Date: 2/13/2013

Event Description

Speaker: Avi Wigderson (IAS, Princeton)

Title: Points, Lines and Ranks of Design Matrices

Abstract: The Sylvester-Gallai theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point (such lines are called "special"), then they must all be on the same line, namely, 1-dimensional. There are many proofs, all elementary. When one moves to the complex numbers the same condition can be met in two dimensions, and Kelly's theorem asserts that the points must lie in a 2-dimensional space. The first proof used algebraic geometry, and a later more elementary proof of this fact is still quite complicated. We prove several extensions and quantitative versions of these theorems (and related ones), in which the assumption is relaxed to having "many" special lines in the given point set (but not all), still imply a constant upper bound on the dimension.

No special background is required. Based on several joint works with Albert Ai, Boaz Barak, Zeev Dvir, Shubhangi Saraf and Amir Yehudayoff.
Location Information:
West Campus - Simons Center for Geometry and Physics  (View Map)
Stony Brook University
Stony Brook, NY 11794
Phone: (631) 632-4459
Room: Room 102

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