Rte 81 2006

All talks will be in 313 Carnegie Library (number 22 on the campus map) on the Syracuse campus. Coffee, muffins, and bagels will precede the first talk and feature prominently in the breaks.

Note: schedule updated 11 Sept.

8:30–9:00

Breakfast (donuts, bagels, coffee provided)

9:00–9:40

Jinjia Li, Syracuse
An elementary proof for a special case of positivity
Show Abstract
Serre defined the intersection multiplicity of two modules (which intersect properly) to be the alternating sum of the length of the Tor modules. Meanwhile, he conjectured that over regular local rings, the intersection multiplicity must be positive when the sum of the dimensions of the two intersecting modules equals the dimension of the ring. We provide an elementary proof for the above positivity conjecture in the special case that one of the intersecting modules has dimension at most one.

9:45–10:25

Sean Sather-Wagstaff, Kent State
Uniform annihilators for local cohomology
Show Abstract
Let (R,m) be a local ring and let J denote the intersection of the annihilators of the local cohomology modules H^i_m(R) for i = 0,...,dim(R)-1. We will provide a new proof of the following recent result of C. Zhou: If R is excellent and equidimensional, then J is not contained in any minimal prime of R. This is joint work with Lars W. Christensen.

10:25–10:55

Break

10:55–11:35

Alina Iacob, North Carolina at Wilmington
DG-injective complexes
Show Abstract
We give a characterization of rings for which every direct sum of DG-injective complexes is DG-injective. We prove that for a commutative local ring the class of DG-injective complexes is closed under direct sums if and only if the ring is noetherian and has finite global dimension. We use this to show that the result holds for any commutative ring of finite Krull dimension.

11:40–12:10

Mauricio Velasco, Cornell
The homogeneous coordinate rings of Del Pezzo surfaces
Show Abstract (PDF)

12:10–2:00

Lunch

2:00–2:40

Amanda Beecher, SUNY Albany
A combinatorial description of the free resolution for multigraded modules
Show Abstract
It is an open problem to explicitly construct the minimal free resolution for a multigraded module. It is known for some special classes of monomial ideals and shown by Charalambous and Tchernev for a certain class of multigraded modules. Tchernev constructs a free resolution which is nonminimal in general, for any finitely presented multigraded module using the theory of matroids. Using such combinatorial methods leads us to ask, is there a combinatorial description of the vector spaces used in his construction? We answer this in the affirmative by associating to these T-spaces, as Tchernev calls them, a certain homology group of the reduced broken circuit complex associated to the matroid. We find that the dimension of the vector T-spaces is a combinatorial invariant called Crapo's beta invariant which has been extensively studied in combinatorial contexts.

2:45–3:25

Tim Clark, SUNY Albany
On the minimal free resolution of a class of monomial ideals
Show Abstract
We study a construction of Tchernev in which a complex of vector spaces is built from the structure of a finite lattice $L$. When $L$ is the lcm-lattice of a monomial ideal $I$, this complex of vector spaces can be transfomed into a complex $\mathbb{F}$ of free multigraded modules that approximates the minimal free resolution of the module $R/I$. Further, we define the class of \emph{lattice-linear} monomial ideals and show that $\mathbb{F}$ is the minimal free resolution of the module $R/I$ if and only if $I$ is lattice-linear.

3:25–3:55

Break

3:55–4:35

Achilleas Sinefakopoulos, Cornell
On Borel-fixed ideals generated in one degree
Show Abstract
We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in $S=\Bbbk[x_1,x_2,...,x_n]$; this includes the case of powers of the homogeneous maximal ideal $(x_1,x_2,...,x_n)$ as a special case. In our most general result we prove that for any Borel fixed ideal $I$ generated in one degree, there exists a polyhedral cell complex that supports a minimal free resolution of $I$.

4:40–5:20

Hara Charalambous, Aristotle University of Thessaloniki
Minimal systems of binomial generators and the indispensable complex of a toric ideal
Show Abstract (PDF)

Free parking will be available in the Quad 3 lot next to Carnegie Library (between number 22 and 23 on the campus map).

A group will meet at 7:00 pm on Friday evening in front of the Panda West restaurant on Marshall Street (at the top-left of the campus map) for dinner.

We will organize a group to go to dinner on Saturday night. Please contact Steven P. Diaz if you are interested. Check back here for more details as we sort them out.

If you are interested in finding someone who is interested in sharing a hotel room, please contact Steven P. Diaz as soon as possible. He will pass this information along to others seeking roommates. Don't forget to include relevant information (male/female, smoker/non, etc.).

• Sheraton Syracuse University Hotel
  801 University Avenue
  315-475-3000
  www.sheratonsyracuse.com
  about 5 min. walk, number 44 on the campus map

• Genesee Grande Hotel
  1060 E. Genesee St.
  315-476-4212 or 800-365-4663
  www.geneseegrande.com
  about 15 min. walk due North of campus

• Parkview Hotel
  713 E. Genesee St.
  315-701-2600
  www.theparkviewhotel.com
  about 20 min. walk North and West of campus

• The Marx Hotel
  701 East Genesee St.
  315-479-7000 or 877-the-marx
  www.themarxsyracuse.com
  about 20 min. walk North and West of campus

• Days Inn
  6609 Thompson Road
  315-437-5998
  www.daysinn.com
  about 5 miles

• Comfort Inn
  6491 Thompson Rd
  315-437-0222
  www.choicehotels.com
  about 5 miles

• Econo Lodge University
  454 James St.
  315-425-0015
  www.daysinn.com
  about 5 miles

Click for a (slightly) larger version. The yellow arrow leads to Carnegie Library.

For the curious: average high/low temperatures in Syracuse for this date are 72 and 52 degrees. Record temperatures are 97 and 35.

• Steven P. Diaz, spdiaz@math.syr.edu
• Graham Leuschke, gjleusch@math.syr.edu
• Claudia Miller, cmille06@math.syr.edu