Fri, November 12, 2021
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5:00pm [5:30pm] Seyed Amin Seyed Fakhari, University of Tehran, Tehran, Iran.
Description:
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

6:00pm