« A Talk on the Diameters of Commuting Graphs of Matrix Rings
A Talk on the Diameters of Commuting Graphs of Matrix Rings
March 09, 2022, 12:15 PM - 1:15 PM
Location:
Mathematics Graduate Student Lounge -- 7th Floor
Rutgers University
Hill Center
Mathematics Department
110 Frelinghuysen Road
Piscataway, NJ 08854
Kayla Gibson, Rutgers University
A commuting graph of a ring is a graph whose vertices are non-central elements of the ring. 2 distinct vertices x and y are said to be adjacent if and only if xy=yx in the ring. I will be discussing the commuting graph of the ring of matrices. We can say some interesting things about the size of the diameter of this graph (when it is connected). I will go through some examples to become comfortable working with these structures. Then I will go over some interesting proofs and results in this field as well as discussing some open problems in the area. This talk will rely pretty heavily on linear algebra.
This seminar is being held in person in The Hill Center, Mathematics Graduate Student Lounge - 7th Floor
and online via a simultaneous broadcast on Zoom.
Zoom Link: https://rutgers.zoom.us/j/97874103984?pwd=VkExb002UFFyMmQvUXYxdFVEQzdOdz09
Meeting ID: 978 7410 3984
Password: 222507