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. |