Conference Travel Funding: "Invariant Theory and its Interactions with Related Fields"

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AbstractAward: DMS-0309788Principal Investigator: Kathryn LeshThis award will provide funding to partially defray travelexpenses of U.S.-based mathematicians attending the conference"Invariant Theory and its Interactions with Related Fields"(Ingo2003), to be held in Goettingen, Germany, March 23-29,2003. Invariant theory, with roots in the 17th century, hasproven to be a robust area of mathematical endeavor. Over thecourse of the last 50 years, it has found new applications inalgebraic topology, representation theory, algebraic geometry, aswell as many traditional areas such as number theory andcommutative algebra. Professor Lesh is on the scientificorganizing committee for Ingo2003, which is an initiative ofresearch groups in Aberdeen, Manchester, and Goettingen workingin the areas of algebraic topology, representation theory, andcommutative algebra. These scientists have found thatcommunication across narrow specialty boundaries can bring greatscientific benefits. A central theme of the conference will bethe many connections of invariant theory to other fields. In thepast, conferences organized around the topic of invariant theoryhave tended to be rather specialized, for example, concentratingon computational aspects, or emphasizing interaction with at mostone other subject area, such as algebraic topology. Ingo2003 isbeing organized with a much broader scientific base and will beinterdisciplinary in a global sense, as well as having a specificfocus on younger researchers. Some of the topics represented indiscussions will be modular representation theory, coinvariantsand the "hit problem," algebraic topology, and Hasse-Schmidtdifferentials and differential Galois theory.One aspect of invariant theory is studying the question of whatelements of a changing situation must in fact remain fixed. Forexample, the points along the axis of a spinning globe remain inthe same position as the globe turns. The point at the center ofthe spindle of a tape player stays fixed while other points onthe spindle turn around it. More surprisingly, rotating a circlearound its center and then flipping the circle over any linethrough its center must leave a different line in a fixedposition. The search for such "invariant" or "fixed" elements ofa situation can be very subtle, and it arises in a wide varietyof mathematical problems and physical applications. The goal ofthe Ingo2003 conference is to allow mathematicians from differingmathematical disciplines to learn techniques from each other, andto disseminate sets of mathematical tools developed in onediscipline to other disciplines that might find them useful.