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Daily Overview |
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RAG4: Real Algebraic Geometry Location: M629 Session Chair: Daniel Plaumann Session Chair: Claus Scheiderer | |
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Positivstellensätze for symmetric functions 1: Universität Konstanz, Germany; 2: UiT The Arctic University of Norway, Norway In this talk, we consider symmetric functions which, under the truncation of variables, can be identified with sequences of symmetric polynomials in all numbers of variables. We call a symmetric function nonnegative (positive) if all associated symmetric polynomials are nonnegative (positive). In general, deciding whether symmetric functions are nonnegative is non-trivial and actually requires verification of a polynomial's nonnegativity on a set that is not semialgebraic. In recent work by Chandrasekaran and Levin such problems have been called any-dimensional problems and it was asked whether Positivstellensätze for this setting exist. As a first step we prove certain analogues of Pólya's and Reznick's Positivstellensätze. | |
