Speaker: Seyed Amin Seyed Fakhari, University of Tehran, Tehran, Iran.
Date/Time: 12 November 2021, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/mgo-iemn-dra
Title: Homological properties of symbolic powers of cover ideals of graphs.
Abstract: To every simple graph one associates its edge ideal which is
generated by quadratic squarefree monomials corresponding to edges of the
graph. In this talk, we study the Alexander dual of edge ideals, which is
called the cover ideal. The reason for this naming is that the cover ideal
is minimally generated by squarefree monomials corresponding to the
minimal vertex covers of the given graph. We review the recent results
about the symbolic powers of cover ideals. In particular, we characterize
all graphs with the property that every symbolic power of its cover ideal
has a linear resolution. Also, we determine an upper bound for the
regularity of symbolic powers of certain classes of graphs including
bipartite graphs, unmixed graphs and claw-free graphs. Moreover, we study
the asymptotic behavior of depth of symbolic powers of cover ideals.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar