[Colloquium] Narayanan/MS Presentation/Feb. 13, 2006

[Margaret Jaffey]

This is an announcement of Hariharan Narayanan's MS Presentation.

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Date:  Monday, February 13, 2006

Time:  2:30 p.m.

Place:  Ryerson 251

M.S. Candidate:  Hariharan Narayanan

M.S. Paper Title:  Volumes of codimension one manifolds and a  
randomised polynomial-time
algorithm for computing the surface volume of a smooth convex body

Abstract:

   In this thesis we develop estimates for volumes of smooth
   boundary manifolds by deriving explicit relations between
   a heat flow across the surface and its volume.

   Applying these estimates together with existing results on
   randomised volume computation and rates of rapidly mixing chains on
   convex sets, we are able to derive a randomised algorithm for
   computing the surface volume of a smooth convex body $M$, that runs
   in time that is polynomial in the dimension $d$, a smoothness
   parameter (the ``condition number") $1/\tau$ and inverse error
   $1/\epsilon$.
   We also include a brief survey of known results related to  
computing the
   volume and surface area of a convex body.

Advisor:  Prof. Partha Niyogi

A draft copy of Hari Narayanan's MS Paper is available in Ry 161A.


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Margaret P. Jaffey                             margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 161A)        (773) 702-6011
The University of Chicago                  http://www.cs.uchicago.edu
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