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 National Science
Foundation Award #0535305 |
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Workshop on Asymptotic Geometry in Paris |
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| Investigator(s): |
Elisabeth Werner (PI)
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| Sponsor: |
Case Western Reserve University, OH 44106 2163684510
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| Start Date/Expiration Date |
2006-01-01 to 2006-12-31 (amended 2005-12-22) |
| Awarded Amount to Date: |
$20,000 |
| Abstract: Abstract
Award: DMS-0535305
Principal Investigator: Elisabeth Werner
This award supports travel of US participants to a "Workshop on
Asymptotic Analysis and Applications" in July 2006 at the
Institut Henri Poincare in Paris, France. The workshop is a
component of the special trimester research program there on
"Phenomena in Large Dimensions" and concerns properties of
families of finite-dimensional objects as the dimension grows
without bound. Particular topics that fit this agenda are
measure transport techniques, concentration of measure,
quantitative measures of convex bodies, isoperimetric
inequalities, and large deviation inequalities. Some of the
important features emerging in these studies are threshold or
phase transition effects, similar to those seen in statistical
physics or asymptotic combinatorics, and this work also seems to
have connections to problems in computational complexity.
A mathematical description of a scientific or engineering
question often requires lots of independent numbers, leading to a
geometric space of high dimension. For example, if you want to
specify the location of one gas molecule in a room then you need
to report the front/back, side-to-side, and up/down locations of
the molecule, using three numbers. The direction and speed of the
molecule's motion takes another three numbers, and so to describe
enough of the molecule's current state to allow us to predict its
future motion from position and velocity we would need six
separate numbers in all. If you want to track 100 distinct
molecules of the air in the room then you will need 600
independent numerical coordinates to collect all of the relevant
measurements. As these dimensions increase then the difficulty
of sampling and computation go up rapidly, a phenomenon
scientists and mathematicians sometimes call "the curse of
dimensionality." However, there are also patterns that emerge as
dimension increases, and this grant for support of US travel to
the international workshop described above will study some of
these patterns that are recent discoveries. |
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| NSF Org: |
DMS - Division of Mathematical Sciences |
| Award Number: |
0535305 |
| Award Instrument: |
Standard Grant |
| Program Manager: |
Christopher W. Stark
DMS Division of Mathematical Sciences
MPS Directorate for Mathematical & Physical Sciences
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| NSF Program(s): |
GEOMETRIC ANALYSIS |
| Field Application(s): |
Other nsf.applications NEC |
| Program Reference Code(s): |
CONFERENCE AND WORKSHOPS, 7556
UNASSIGNED, 0000 |
| Program Element Code(s): |
1265 |
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