UIUC Dept. of Mathematics Seminar Calendar

      April 2012              May 2012              June 2012      
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
  1  2  3  4  5  6  7          1  2  3  4  5                   1  2
  8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
 15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
 22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
 29 30                  27 28 29 30 31         24 25 26 27 28 29 30

Thursday, May 3, 2012

Special Graduate Geometry and Topology Seminar
12:00 pm in 241 Altgeld Hall, Thursday, May 3, 2012

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Submitted by lukyane2.

Amir Nayyeri (UIUC Computer Science)
How to Walk Your Dog in the Mountains
Abstract: We describe a O(log n)-approximation algorithm for computing the homotopic Frechet distance between two polygonal curves that lie on the boundary of a surface. Prior to this work, algorithms where known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a $O(\log n)$-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic Frechet distance, or the minimum height of a homotopy, is in NP. Joint work with Sariel Har-Peled, Mohammad Salavatipour and Anastasios Sidiropoulos

Geometry Seminar
3:00 pm in 347 Altgeld Hall, Thursday, May 3, 2012

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Submitted by sba.

Joseph Rosenblatt (UIUC)
Partitions for Optimal Approximations
Abstract: The Riemann integral can be approximated using partitions and a rule for assigning weighted sums of the function at points determined by the partition. Approxi- mation methods commonly used include endpoint rules, the midpoint rule, the trapezoid rule, Simpson’s rule, and other quadrature methods. The rate of approximation depends mostly on the rule being used and the smoothness of the function, but fine structure in this rate of approximation depends on choosing an optimal partition. We discuss how one chooses an optimal partition of points, what is the resulting rate of approximation as the number of points tends to infinity, and how to determine the characteristic distribution of the points in these optimal partitions.