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Some problems on affine semigroups
Student-Run Research Seminar| Speaker: | Pierre Dueck, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Jan 31 2007, 12:10PM |
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.