Principal Investigator: Kathryn Lesh
This award will provide funding to partially defray travel expenses 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, has proven to be a robust area of mathematical endeavor. Over the course of the last 50 years, it has found new applications in algebraic topology, representation theory, algebraic geometry, as well as many traditional areas such as number theory and commutative algebra. Professor Lesh is on the scientific organizing committee for Ingo2003, which is an initiative of research groups in Aberdeen, Manchester, and Goettingen working in the areas of algebraic topology, representation theory, and commutative algebra. These scientists have found that communication across narrow specialty boundaries can bring great scientific benefits. A central theme of the conference will be the many connections of invariant theory to other fields. In the past, conferences organized around the topic of invariant theory have tended to be rather specialized, for example, concentrating on computational aspects, or emphasizing interaction with at most one other subject area, such as algebraic topology. Ingo2003 is being organized with a much broader scientific base and will be interdisciplinary in a global sense, as well as having a specific focus on younger researchers. Some of the topics represented in discussions will be modular representation theory, coinvariants and the "hit problem," algebraic topology, and Hasse-Schmidt differentials and differential Galois theory.
One aspect of invariant theory is studying the question of what elements of a changing situation must in fact remain fixed. For example, the points along the axis of a spinning globe remain in the same position as the globe turns. The point at the center of the spindle of a tape player stays fixed while other points on the spindle turn around it. More surprisingly, rotating a circle around its center and then flipping the circle over any line through its center must leave a different line in a fixed position. The search for such "invariant" or "fixed" elements of a situation can be very subtle, and it arises in a wide variety of mathematical problems and physical applications. The goal of the Ingo2003 conference is to allow mathematicians from differing mathematical disciplines to learn techniques from each other, and to disseminate sets of mathematical tools developed in one discipline to other disciplines that might find them useful.
