[Colloquium] REMINDER: today's talk by Jack H. Lutz

[Margery Ishmael]

DEPARTMENT OF COMPUTER SCIENCE - TALK
& LOGIC SEMINAR

Date: Friday, October 20, 2006
Time: 2:30 p.m.
Place: Ryerson 251

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Speaker: JACK H. LUTZ

From:  Iowa State University

Url: http://www.cs.iastate.edu/~lutz/

Title:  The Dimensions of Individual Points in Euclidean Space

Abstract:

The recent theory of constructive dimension uses the
theory of computing to assign a dimension to every
{\it individual point} in Euclidean space.  These
dimensions appear to be geometrically meaningful.  For
example, we now know the following:
   1. The {\it classical} Hausdorff dimension of any set
      X that is a union of computably closed sets is simply
      the supremum of the dimensions of the individual
      points x \in X. (work with Hitchcock)
   2. Every point on any computable curve of finite length
      has dimension at most 1 (but not conversely). (work
      with Gu and Mayordomo)
   3. For any point x in any computably self-similar
      fractal F and any sequence T that canonically codes
      the location of x in F, the dimension of x is given
      by dim(x) = dim(F)dim^pi(T), where dim(F) is the similarity
      dimension of F and  dim^pi(T) is the dimension of the sequence  
T with
      respect to a natural probability measure pi induced
      by F. (work with Mayordomo)

This talk will survey these developments and suggest
directions for future research into how the dimensions of
points and related ideas from the theory of computing
interact with geometric measure theory.


***The talk will be followed by refreshments in Ryerson 255***

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Host:  Lance Fortnow

People in need of assistance should call 773-834-8977 in advance.

For information on future CS talks: http://www.cs.uchicago.edu/events

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