Discrete CATS Seminar
####
**
**#####
U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

FALL 2009

##
"Finiteness theorems for chains of toric ideals"

Abraham Martin del Campo

Texas A&M

###
Monday, November 16, 2009

4:00 pm, 845 Patterson Office Tower

####
Abstract:

We study chains of toric ideals that are invariant under a symmetric group
action. In our setting, the ambient rings for these ideals are polynomial
rings which are increasing in (Krull) dimension. Thus, these chains will
fail to stabilize in the traditional commutative algebra sense. However,
we prove a general theorem which says that "up to the action of the
group", these chains stabilize up to monomial localization. This gives a
partial resolution to a conjecture of Aschenbrenner and Hillar.

This is a joint work with Chris Hillar.