[Colloquium] Talk by Jack H. Lutz on Friday, October 20, 2006
Margery Ishmael
marge at cs.uchicago.edu
Fri Oct 13 15:35:38 CDT 2006
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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