Metroplex Algebraic Geometry, Algebra and Number
Theory (AGANT) Seminar, a joint venture of
UNT, UTA
and TCU
Date/Time/Room: Friday (2/3/2012) at 4:30 pm
in 304 Pickard Hall
Speaker: Kristen
A. Beck, Department of
Mathematics, University of
Arizona.
"Depth and Dimension for
High Syzygies"
Abstract: This talk will focus on the
asymptotic behavior of two
invariants, depth and
dimension, for syzygies of a finitely
generated module of
infinite projective dimension over a
commutative local
noetherian ring. It is already known, by
work of Okiyama (1991),
that the depths of such syzygies
eventually stabilize to that of
the ring. This result is
natural, given the intimate connection
between depth and
free resolutions. However, formulating a
similar statement
for dimension is not as straightforward. In
this talk, we
will give necessary conditions for the
stabilization of
dimensions of syzygy modules. In particular, we
will show
that all high syzygies of a module with
eventually
nondecreasing Betti numbers over an equidimensional
ring
have dimension equal to the dimension of the ring.
A map of UTA may be found at
http://www.uta.edu/maps/,
and at http://www.uta.edu/maps/transportation.
The former gives buildings and the latter gives parking lots; both
are interactive. Note that PKH is the triangular building in
the 3 pm position in the former. Select Pickard Hall from the
building selector. PKH is next to the ``garage'' & is on
Nedderman Dr between Planatarium Place (aka College St) & West
St. West St is oneway northbound between W Mitchell St and 3rd
St. Parking is available in the nearby (East and SE of PKH)
parking lots with a UTA permit (but many people park there late on
Fridays with no permit). There are a few metered parking spots on
the East side of Pickard Hall on West St. Visitor (free), &
metered, parking is available by Davis Hall (marked DH in SW part
of the submap). A parking garage (expensive) is nextdoor to PKH
(use West St to get to it). Note that if heading south on Cooper,
then no left turn is allowed to Nedderman Dr. Note that PKH 304
is on the 3rd floor of PKH; turn right out of elevator on 3rd
floor.
Questions, etc on arrangements/directions should be
sent to Dr Vancliff; if
travelling from out of town, notify Dr Vancliff, as we will delay
starting the talk for you if you are late.
