RIMS研究集会
Computational Commutative Algebra and Convex Polytopes

August 1 (Monday) ~ August 5 (Friday), 2016

ABSTRACT

 
August, 1 (Mon) August, 2 (Tue) August, 3 (Wed) August, 4 (Thu) August, 5 (Fri)

9:30--10:30 Volkmar Welker (Philipps-Universität Marburg)
"On the ideal of orthogonal representations of a graph"
  An orthogonal representation of a graph is a map from its vertex set to read d space such that two vertices not connected by an edge are mapped to orthogonal vectors. We study the ideal generated by the obivous equations cutting out orthogonal representations. For d=2 we show that the ideal is radical and prime if and only if G is d-connected.



10:45--11:45 Lukas Katthän (Goethe-Universität Frankfurt)
"Multiplicative structures on minimal free resolutions of monomial ideals"
   The minimal free resolution of a cyclic module over the polynomial ring admits a (generally non-associative) multiplication which satisfies a Leibniz' rule. This multiplication is far from being unique, and in favorable cases it can be choose to be associative, which makes the resolution into a DGA.
 In this talk, I will consider these multiplicative structures in the setting of monomial ideals. On the one hand, I will present some structure theorems about these multiplications, in particular in the associative case. On the other hand, I will show that the presence of an associative multiplication (DGA) has implications on the possible Betti numbers of the ideal.