REU Site in Mathematics at Louisiana State University

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The REU Site in Mathematics at the Louisiana State University will engage a group of twelve nationally selected, highly motivated undergraduates in current mathematical research around the theme: Invariants in Galois Theory, Geometry and Knot theory. To this end we will create an environment with social and scientific activities that nurtures intellectual creativity, encourages mutual support and promotes the discussion, communication and dissemination of mathematical ideas. Participants are introduced to mainstream math problems within the fields of number theory, algebraic geometry and topology which are supported by well-developed symbolical computation software. This provides an early capability to ask significant questions and make computational explorations while theoretical knowledge is being further developed. Additional guidance is provided during mentoring sessions to permit each participant to choose their own project direction at the end of the first week (within the arenas laid out by the introductory presentations during the first week). The REU students are housed on the LSU campus; additional program activities are planned that will foster the interaction of all participants and promote group cohesion. Each student gives several graduated presentations and submits a written paper in a form suitable for publication.Galois theory, algebraic geometry and knot theory lie at the intersection of many threads of current mathematical research connecting geometric problems of the twenty-first century. Algebraic and computation tools are employed to differentiate among the possible geometric structures. We are introducing a new generation of mathematicians to this exciting mix of ideas and providing participants with communication skills suitable to making presentations at conferences as well as advice on making applications to graduate school and on potential career opportunities. By broadening and strengthening the mathematically trained workforce, this REU will do its share to alleviate the current and projected national shortage within the scientific and technological workforce.