| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | October 25, 2010 |
| Latest Amendment Date: | October 25, 2010 |
| Award Number: | 1040754 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Jennifer Pearl
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | November 1, 2010 |
| End Date: | October 31, 2012 (Estimated) |
| Total Intended Award Amount: | $40,000.00 |
| Total Awarded Amount to Date: | $40,000.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
1500 HORNING RD KENT OH US 44242-0001 (330)672-2070 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
1500 HORNING RD KENT OH US 44242-0001 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | INFRASTRUCTURE PROGRAM |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
NSF/CBMS Regional Conference in the Mathematical Sciences, Ergodic Methods in the Theory of Fractals, June 18-23, 2011
Fractal geometry studies closed compact subsets of a Euclidean space. The usual notion of a dimension which is an integer number is replaced by Hausdorff dimension. Fractals play an important role in complex dynamics, mathematical physics, Diophantine approximation and many other areas of mathematics. Ergodic theory studies the behavior of a dynamical system (a compact metric space with a homeomorphism) when it is allowed to run for a long time. Under certain conditions (ergodicity), the time average of a function converges to its space average. Ergodic theory is widely used in many areas of mathematics such as combinatorial number theory, mathematical physics, Lie groups and others.
The main focus of this CBMS conference is to develop Ergodic methods to solve geometric, analytic, probabilistic and combinatorial problems, to call attention of undergraduate and graduate students to a number of topics of common interest to analysts and geometers, and to provide basic instruction in these areas with an emphasis on the fundamental ergodic ideas involved. Particular attention will be drawn to applications of Ergodic Theory to Fractal Geometry (questions involving behavior of fractal sets, measures with uniform scaling scenery, CP processes, Ramsey type results). The interest in the subject is based upon its importance in order to achieve progress in solving different problems related to the Fractal geometry and additive combinatorics.
Hillel Furstenberg is widely known for his application of probabilistic and ergodic methods to other areas of mathematics, including number theory and Lie groups. His talks are true masterpieces that are absolutely self-contained and accessible to anyone - from specialists to graduate and undergraduate students.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The conference was held at Kent State from June 20th till June 27th, 2011. It attracted the attention of many people from different areas of Mathematics from all over the world.
In particular, the schools of participants were from Argentina, Canada, Finland, Hungary, Israel, Spain, Turkey, UK, and USA. In fact, to count "mother tongues", there were participants from 21 countries. There were the representatives of several local schools from Ohio:
Bowling Green State University, Kent State University, Miami University, Ohio University, Ohio State University. The total number of participants was 69, among them 10 female ones, 41 participants were not from Kent State, among them 18 from abroad. There were 32 Graduate Students, 3 Postdocs, 35 participants received the support through the grant.
For any additional information please visit the conference webpage
http://www.kent.edu/math/events/conferences/cbms2011.cfm
Hillel Furstenberg delivered 10 (in fact, 11) wonderful lectures that captured the attention
of the audience from the very beginning. The description of the lectures can be found on
http://www.kent.edu/math/events/conferences/cbms2011/upload/programfurstenberg4.pdf
The lectures were recorded and now are available for general audience, please visit
http://www.kent.edu/math/events/conferences/cbms2011/cbms-lecture-video-and-notes.cfm
Additional speakers were Michael Hochman, (Princeton University, USA), Mark Pollicott,
(University of Warwick, UK), Pablo Shmerkin, (University of Surrey, UK), Karoly Simon,
(Budapest University of Technology and Economics, Hungary), Boris Solomyak, (University
of Washington, USA), Fedor Nazarov, (University of Wisconsin-Madison, USA). The speak-
ers delivered the lectures not only for high mathematical audience, but also for students.
Again, all lectures were recorded and are available online, please visit
http://www.kent.edu/math/events/conferences/cbms2011/cbms-lecture-video-and-notes.cfm
Now the lectures are almost ready for publication and soon will appear as a new wonderful source of ideas from Ergodic Theory and Fractal Geometry. Many students and people from all over the world will learn and benefit from it.
Last Modified: 01/15/2013
Modified by: Dmitry Ryabogin
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