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Mathe-Kolloquium: Abstract zum Vortrag am 22.5.2012
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Fulltext:
Critical points of master functions
Michael Falk
Northern Arizona University
Abstract: We study the critical points of functions
n
i=0 i
i , where 0, . . . , n
are homogeneous linear forms and 0, . . . , n are complex weights satisfying
n
i=0 i = 0. These master functions and their critical points play the central
role in the Bethe Ansatz, which produces eigenvectors for commuting hamiltonians in certain quantum integrable systems.
For generic weights the critical points of are isolated and non-degenerate,
and their number is determined by the combinatorics of the associated hyperplane arrangement. In this talk we will show how a linear syzygy among polynomial master functions gives rise to families of master functions with positivedimensional critical sets. The existence of such syzygies can be characterized
combinatorially in terms of projections of Bergman fans, geometrically in terms
of linear systems of hypersurfaces, and topologically in terms of resonance varieties. Everything will be illustrated with examples, including some arising from
the Bethe Ansatz and some new examples involving arrangements arising from
graphs.
Math_Colloquium: Abstract to the Talk at 5/22/2012
Mathe-Kolloquium: Abstract zum Vortrag am 22.5.2012
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DRUCKEN 
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