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Some problems on affine semigroups
Student-Run Research| Speaker: | Pierre Dueck, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Jan 31 2007, 12:10PM |
Description
An affine semigroup is a sub-semigroup of R^d generated by finitely many
vectors. Such semigroups provide a basic link between combinatorics and
commutative algebra, via their toric ideals. Using tools from commutative
algebra, we exhibit structural properties of low-codimension semigroups,
allowing us to compute a basic invariant, the Caratheodory Rank for these
examples. In general, we have the bound d \leq C.R. \leq 2d-2, were d is
the dimension of the semigroup, however we do not yet have an algorithm to
compute the Caratheodory Rank of specific examples. This brings us to
several interesting open problems in the subject. This is joint work with
Serkan Hosten.