Computational Representation Theory in Number Theory

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This award provides partial participant support for the workshop "Computational Representation Theory in Number Theory" held July 27-31, 2015 at Oregon State University in Corvallis, Oregon. This workshop will promote the generation and dissemination of current research in computational number theory related to representation theory. In particular, it will foster research collaboration between senior and junior researchers. The workshop will also address the need for access to recent computational data in these areas by disseminating results through the L-functions and Modular Forms Database (LMFDB), located at http://www.lmfdb.org/. This website serves the mathematical community by providing data that is the result of rigorous computations of mathematical objects of interest in the modern number theory community, as well as by playing an educational role for students and researchers interested in number theory.The theme of this workshop is the connection between types of representations, particularly Galois representations, and other objects of interest in number theory, including L-functions and elliptic curves, with a focus on computation. The workshop includes lectures on Artin representations, integral representations, mod p Galois representations, and l-adic representations. The workshop is intended to advance research in computational representation theory, particularly Galois representations and their applications to number theory. This workshop will also foster collaboration between experts and junior researchers in these areas. The workshop will be a hybrid of typical conference and workshop formats. The mornings will be dedicated to invited research talks and the afternoons will be dedicated to work in small groups. During the afternoon sessions groups will work on research questions, generating computational data, or presenting computational work to the public through the L-functions and Modular Forms Database (LMFDB). More details can be found at http://people.oregonstate.edu/~swisherh/CRTNTconference/index.html.