Fri, February 4, 2022
Public Access Category: All |
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- Time:
- 6:30pm
- 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/vcc-aywh-xgx
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 Castelnuovo-Mumford regularity of these ideals.
For more information and links to previous seminars, visit the website
of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar