2017 CMS Winter Meeting

Waterloo, December 8 - 11, 2017

Applications of Combinatorial Topology in Commutative Algebra
Org: Sara Faridi (Dalhousie University) and Adam Van Tuyl (McMaster University)

ARINDAM BANERJEE, Purdue University, USA

MINA BIGDELI, IPM, Iran

GIULIO CAVIGLIA, Purdue University, USA

ALEXANDRU CONSTANTINESCU, Freie Universitaet Berlin, Germany

FEDERICO GALETTO, McMaster University
Distinguishing k-configurations  [PDF]

A $k$-configuration in the projective plane is a collection of points, subject to certain geometric conditions, introduced by Roberts and Roitman to study Hilbert functions of graded algebras. If $d$ is the maximal number of colinear points in a $k$-configuration, then there can be anywhere between 1 and $d+1$ distinct lines containing exactly $d$ points of the $k$-configuration. The number of such lines is not detected by the usual invariants of the defining ideal of the $k$-configuration. Instead, I will illustrate how this number of lines is encoded in the Hilbert function of a high enough symbolic power of the defining ideal of the $k$-configuration. This talk is based on joint work with Y.S. Shin and A. Van Tuyl (arXiv:1705.09195).

TAI HA, Tulane University, USA

MARTINA JUHNKE-KUBITZKE, University of Osnaebruck, Germany

SUSAN MOREY, Texas State University, USA

SATOSHI MURAI, Osaka Universy, Japan

CONNOR SAWASKE, University of Washington, USA