UTA Department of Mathematics

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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 non-decreasing 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 one-way 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.



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