Seminar Details
A Talk on the Diameters of Commuting Graphs of Matrix Rings
- Start Date: March 9, 2022
- Event Start Time: 12:15 PM
- Event End Time: 1:15 PM
- Seminar Series: Graduate Combinatorics Seminar
- Presenter(s): Kayla Gibson - Rutgers University
- Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
- Event Additional Info: <p>This seminar is being held in person in The Hill Center, Mathematics Graduate Student Lounge - 7th Floor<br /> and online via a simultaneous broadcast on Zoom.<br /> Zoom Link: <a href="https://rutgers.zoom.us/j/97874103984?pwd=VkExb002UFFyMmQvUXYxdFVEQzdOdz09" target="_blank">https://rutgers.zoom.us/j/97874103984?pwd=VkExb002UFFyMmQvUXYxdFVEQzdOdz09</a></p> <p>Meeting ID: 978 7410 3984</p> <p>Password: 222507</p>
- Presentation Type: Stand Alone Presentation
- Abstract:
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.