The Year of Algebra 2002- 2003 at the University of Florida is highlighted by the celebration of the 70th birthday of John G. Thompson. The general theme of the Year of Algebra is provided by the wider context of Thompson's monumental contributions: the beauty and power of group theory, and how it applies to problems of arithmetic via the basic principle of Galois. The Year of Algebra features a conference in Galois Theory (Nov. 3--9, 2002), a conference in Group Theory (March 9--16, 2003) and a workshop on Computational Aspects of Algebraic Curves, and Cryptography (March 9--15, 2003). The Galois conference centers around the Inverse Problem of Galois Theory, one of the major open problems of mathematics. The conference on Finite Group Theory has speakers involved in the completion/ revision of the Classification, as well as speakers in Representation Theory, and applications of Finite Groups to Finite Geometries and other areas. The workshop deals with interactions between modern computational tools/questions and the theory of algebraic curves, emphasizing the application to public key cryptography. It has a strong instructional component (mini-courses).
Group Theory is the abstract study of symmetry patterns (of any object), and Galois Theory provides tools for applying Group Theory to algebra and arithmetic. Recent applications to data security (public key cryptography) are the topic of the workshop. Galois Theory and Group Theory have further applications to physics, chemistry and coding theory. The Year of Algebra provides an opportunity for young mathematicians, women and minorities to learn the latest advances. It was John G. Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification, it was again J. Thompson who led the way in exploring its implications for Galois Theory. For these contributions, Thompson has recently been awarded the National Medal of Science. He also won the Fields Medal, the highest honor in mathematics. For the Year of Algebra, University of Florida Graduate Research Professor John G. Thompson acts as an advisor. His powerful ideas continue to inspire the young. We want to use this opportunity in a special effort to integrate research and education during the Year of Algebra. While the two conferences emphasize latest advances in research, the workshop has a strong instructional component.
