Invited Speakers

• Alexander Bobenko, Technische Unversitaet Berlin: Glueing a convex polytope: a constructive proof of Alexandrov's theorem

  We present a constructive proof of Alexandrov's theorem on existence of a convex polytope with a given metric on the boundary. The idea is to do a deformation in the class of so called generalized convex polytopes with positive curvature. The proof gives rise to a numerical algorithm that was implemented in a computer program which will be demonstrated. (Joint work with Ivan Izmestiev)

• Timothy Chan, University of Waterloo: Computational Geometry on the Word RAM

  In this talk, I will describe recent advances in geometric algorithms on the "transdichotomous" word RAM model. Algorithms that can sort n integers in time better than the comparison-based n log n lower bound have been known for quite some time. I will show that many of the favorite problems in our field---for example, 3-d convex hulls, 2-d Voronoi diagrams, line-segment intersection, and offline point location---can also be solved in o(n log n) time for integer input. At least one interesting recurrence will be encountered, open problems will be mentioned, and issues concerning the word RAM vs. the more "traditional" real RAM will be discussed. (Joint work with Mihai Patrascu)

• Martin Demaine, MIT: Mathematics is Art

  This talk will describe my explorations in art and mathematics and their interrelation. Both art and mathematics are founded on the power of creativity and ideas, followed by precise execution within the medium. Topics include glass blowing, performance art, puzzles, origami, architecture, and hinged dissections. In addition to being entertaining, this talk will announce and describe a new solution to an open problem.

• Robert Ghrist, University of Illinois: Euler characteristic for data aggregation

  This work is motivated by a fundamental problem in sensor networks -- the need to aggregate redundant sensor data across a network. We focus on a simple problem of counting targets with a network of sensors that can count nearby targets, but cannot identify or localize them.

  We show a clear, clean relationship between this problem and the topology of constructible sheaves. In particular, an integration theory from sheaf theory that uses Euler characteristic as a measure provides a computable, robust, and powerful tool for data aggregation. (Joint work with Y. Baryshnikov, Alcatel/Lucent)