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[6:30pm] Adam Van Tuyl, McMaster University
 Description:
 Speaker: *Adam Van Tuyl, McMaster University, Canada*Date/Time: *4* February 2022*,
6:30pm IST/ 1:00pm GMT / 8:00am ET *(joining time 6:15pm IST)
Gmeet link: meet.google.com/vccaywhxgx
Title: Toric ideals of graphs and some of their homological invariants
Abstract: The study of toric ideals of graphs lies in the intersection of
commutative algebra, algebraic geometry, and combinatorics. Formally, if $G
= (V,E)$ is a finite simple graph with edge set $E =\{e_1,\ldots,e_s\}$ and
vertex set $V = \{x_1,\ldots,x_n\},$ then the toric ideal of $G$ is the
kernel of the ring homomorphism $\varphi:k[e_1,\ldots,e_s] \rightarrow
k[x_1,\ldots,x_n]$ where $\varphi(e_i) = x_jx_k$ if the edge $e_i =
\{x_j,x_k\}$. Ideally, one would like to understand how the homological
invariants (e.g. graded Betti numbers) of $I_G$ are related to the graph
$G$. In this talk I will survey some results connected to this theme, with
an emphasis on the CastelnuovoMumford regularity of these ideals.
For more information and links to previous seminars, visit the website
of VCAS: https://sites.google.com/view/virtualcommalgebraseminar

