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New Change of Major Policy. Next Open Period: July 31,2017 - September 1, 2017
The 39th Virginia Tech Regional Math Contest with be held 9:00am - 11:30am on Saturday, October 21.
Featured ResearchEyvindur Palsson - A fundamental question in big data is finding, counting and classifying patterns. Distance is one of the simplest patterns. The classical Falconer distance problem can be stated as follows: How large does the Hausdorff dimension of a set need to be to ensure that the Euclidian distance set has positive one-dimensional Lebesgue measure? This problem can be viewed as a continuous analogue of the Erdös distinct distance problem. In the combinatorics literature analogues of the Erdös distinct distance problem for more complicated patterns have been studied for decades. Examples include angles, triangles and areas of triangles. These more complicated patterns similarly give rise to Falconer type questions. Professor Palsson has established a number of Falconer type theorems for triangles and higher order configurations. He has also flipped the question and studied configurations where distances are given and the question is whether a configuration exists that realizes those distances. This question connects to the existence of crystals. As a step in understanding such questions Professor Palsson classified all possible 5 point crescent configurations that relate to an open problem of Erdös on the existence of crescent configurations.
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