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Abstract:
Erd\'elyi's work on hypergeometric functions
in the 1950s raises fundamental questions about the
number of holomorphic solutions to classical Horn
systems. Techniques developed by Gelfand, Kapranov,
Zelevinsky, and others in the 1980s and 1990s
successfully deal with series solutions having full
support (where the set of monomials with nonzero
coefficients fills a cone of the maximum possible
dimension) by constructing D-modules out of prime
binomial ideals. In work with Alicia Dickenstein and
Laura Matusevich, we deal with all holomorphic solutions
by using arbitrary binomial ideals, especially
combinatorial descriptions of their primary
decompositions.
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