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

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

Date

Fri, February 4, 2022

Start Time

6:30pm IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Fri, February 4, 2022 3:10pm IST