On taking the right path with the world of graph theory: Meet Mahsa N Shirazi, our PIMS CRG PDF, University of Manitoba.
By Lisa Sammoh, Communications and Events Assistant.
Mahsa N Shirazi is currently doing her postdoctoral fellowship at the University of Manitoba. She completed her bachelor’s and master’s degree at the Shiraz University of Technology in Iran. Mahsa didn’t always know she would become a mathematician; she spent a lot of time in her third year as an undergraduate deciding whether to pursue mathematics or fine arts. “I liked them both very much”, she admits. Eventually, she chose a math major, but it wasn’t until her graduate studies where, for the first time, she had a taste of conducting research, and realised she had made the right choice. Mahsa’s growing interest in linear algebra and graph theory led her to connect with other researchers in the area. She reached out to Profs. Shaun Fallat and Karen Meagher (URegina) after reading their papers and becoming intrigued with their research work. Currently, her interest in mathematics is centred around the world of graph theory, where she conducts her postdoctoral research under the supervision of Karen Gunderson (UManitoba). We connected with Mahsa to learn more about her academic work, and what life in Winnipeg has been like so far.
Tell us about your academic journey; what field are you in and how did you connect with your current PDF supervisor Karen Gunderson at the University of Manitoba?
My research interests lie primarily in graph theory, matrix theory, and combinatorics. These three areas are tightly connected and complement each other. I am fascinated by the fact that one can understand and solve a graph theory problem by exploring the corresponding matrix problems and vice versa.
I did my bachelor’s degree in pure mathematics at the Shiraz University (Iran). I also obtained an MSc degree in numerical linear algebra at the Shiraz University of Technology under the supervision of Behnam Hashemi. I worked on some linear algebra problems over semirings and their connections to graph theory. From there, I wanted to focus on learning more about the world of graph theory, and ended up emailing Profs. Shaun Fallat and Karen Meagher (URegina). I had read some of their papers before and was very interested in their research works. So after expressing my interest in pursuing my PhD under their supervision, they agreed that I apply for a position at the University of Regina.
I began my PhD program in 2018, where I concentrated more on algebraic graph theory. In my main research project, I used graph theory to answer a family of questions that arise in Design theory. In particular, my thesis was on extensions of the famous Erdös-Ko-Rado (EKR) theorem to perfect matchings and uniform set partitions. Such results give the size and structure of the largest set of t-intersecting objects. Our results can be found in two published papers and a submitted article: “The Erdös-Ko-Rado theorem for t-intersecting families of perfect matchings”, with Shaun Fallat and Karen Meagher, “An extension of the Erdös-Ko-Rado theorem to uniform set partitions”, with Karen Meagher and Brett Stevens, and “ An extension of the Erdös-Ko-Rado theorem to set-wise 2-intersecting families of perfect matchings” (single-author).
In addition, as part of the Discrete Math Research Group (DMRG) of the University of Regina, I have done some research work on combinatorial matrix theory. An interesting question in spectral graph theory is about the structure of the eigenvectors of matrices associated with graphs. In one of our projects, we studied graphs for which their Laplacian matrix can be diagonalized with a weakly Hadamard matrix. The results can be found in the paper, “Weakly Hadamard Diagonalizable Graphs”.
Around that time, I also attended different conferences and workshops, including the “7th Graph Searching in Canada” (GRASCan) workshop in Regina. I first met my current postdoctoral fellowship supervisor, Karen Gunderson, at GRASCan. She gave a wonderful talk on “Finding small percolating sets”. I had several more encounters with her at different conferences (both online and in-person), and by the time my graduation was coming around, she informed me about an opening for a postdoctoral position with the PIMS CRG on Movement and Symmetry on Graphs. I took my chance to apply for the position and got an offer!
In our current project, Karen and I are working on a special type of strongly regular graphs called friendship graphs. Also, as part of the DMRG group, I am able to collaborate with Karen Gunderson, Karen Meagher, and Joy Morris, where we are working on an extremal graph theory problem related to the EKR problem.
Are you teaching this semester, or did you do so in the previous semester? If so, what courses did you teach? What was the experience like, and was there anything you learned or took from it?
I taught a course in Combinatorics (of course, my favourite topic to teach!) in Fall 2022. This was the first semester after COVID-19 at the University of Manitoba and classes were starting to be held in person again. Teaching the course in person was a nice experience; it was fun to see the reactions on the students’ faces when they finally understood a topic. I was lucky to have active students as well; one of them, Karan, ended up doing a project as part of the PIMS Virtual Experimental Math Lab (VXML) program. This semester, I am co-supervising Karan and another student, Anu (an undergraduate student from the University of Saskatchewan), with Ragu who is also a postdoctoral fellow at the University of Regina.
What do you do to balance your research and life, and what does a typical Sunday look like for you?
On weekends I try to have at least one day off work to relax, have a video call with my family, and meet my friends. On some Sunday mornings, I also meet up with a group of friends for an arts and crafts gathering and lunch afterwards. I also like to go out and try some outdoor activities. One of my favourite places to spend my weekend mornings and get breakfast in Winnipeg is The Forks. It is near the Red and Assiniboine Rivers, and during winter, people can skate on the river. It is fun! Though Sunday evenings are not as fun as the mornings, I usually spend them preparing for the coming week by meal prepping and completing house errands.
Mahsa N Shirazi is a PIMS-CRG postdoctoral fellow at the University of Manitoba, under the supervision of Karen Gunderson. Her research is centered around using graph theory to answer questions that arise in design theory. Her current research project is on a special type of strongly regular graphs called r-friendship graphs. She is also interested in EKR problems on different mathematical objects, like perfect matchings and uniform set-partitions. She is also interested in Matrix theory and linear algebra.
She completed her Ph.D. at the University of Regina under the supervision of Shaun Fallat and Karen Meagher. Her main PhD research was on the extensions of the famous Erdös-Ko-Rado theorem to t-intersecting families of perfect matchings in graphs. She obtained her master’s degree in numerical linear algebra at the Shiraz University of Technology, under the supervision of Behnam Hashemi. Besides research and studying, she also enjoys painting and baking.
Mahsa will be speaking at the PIMS Emergent Research Seminar Series, on February 8, 2023, at 9:30 AM Pacific. Details on her talk and poster, Extensions of the Friendship Theorem, can be found here.
