Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference

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The 2007 Midwest Geometry Conference included a panel discussion devoted to open problems and the general direction of future research in fields related to the main themes of the conference. This paper summarizes the comments made during the panel discussion.
This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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