Workshop for new faculty and graduate students on Lattice-Ordered Groups and MV-Algebras

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Principal Investigator: McGovern, Warren Wm.Proposal Number: 0901560Institution: Bowling Green State UniversityTitle: Workshop for new faculty and graduate students on Lattice-Ordered Groups and MV-AlgebrasAbstract: The Department of Mathematics and Statistics at Bowling Green State University (Ohio, USA) will host a workshop on lattice-ordered groups and MV-algebras June 8th through June 12th. The workshop will provide a very important opportunity to new researchers (including graduate students) to work with experts from the two fields. The workshop will be followed by the 12th annual International Conference on Ordered Algebraic Structures which will run from the 15th of June through the 19th of June. The theory of lattice-ordered groups has a long history and has many applications to other branches of mathematics: lattice theory, permutation groups, commutative integral domains, vector lattices, positivity, algebraic K-theory, and general topology. MV-algebras (or ?many-valued algebras?) were introduced in the 1950s by C.C. Chang to form the algebraic semantics of Lukasiewicz many-valued logic. The theory of MV-algebras has applications to logic, toric varieties, algebraic K-theory, functional analysis, and C*-algebras. In 1986, D. Mundici proved that the category of abelian lattice-ordered groups with strong order unit and their unit-preserving homomorphisms is naturally equivalent to the category of MV-algebras. In 2002 this result was extended to a natural equivalence between the category of lattice-ordered groups with strong order unit and their unit-preserving homomorphisms and the category of generalized MV-algebras (a.k.a. pseudo MV-algebras).The workshop aims to inform its participants on the recent breakthroughs of how the two branches of mathematics interact with each other. It is hoped that the workshop will lead to further developments and connections between the two fields. One of the main goals of the workshop is to expose new faculty and graduate students, including members of under represented groups, to the two branches of mathematics and have them interact with experts in the fields. The participants will also be afforded the opportunity to participate in the 12th annual International Conference on Ordered Algebraic Structures which immediately follows the workshop. For more information about the workshop, please see the following webpage:http://www-math.bgsu.edu/~warrenb/Workshop/Workshop09.html