Yesterday, Wednesday May 28, my first Ph.D. student defended her thesis: Theresa Migler-VonDollen. Although you can’t tell from the picture, attendance at this was the highest any of us had seen — 15 to 20 graduate students were lined up along the wall of the seminar room. It’s a testament to how loved Theresa has been — ever helpful, being the unofficial math and algorithms tutor for all the graduate students in the department — and almost always with a big smile on her face.
Theresa’s dissertation is on observations of the hierarchy of density of real networks, such as (but not limited to) social networks. The hierarchy came out of an early proof of correctness of finding a lexicographically minimum orientation of undirected graphs (finding an orientation of the graph that minimizes the indegree sequence lexicographically). You can read a sampling of her work in our first manuscript on this where we show that the density hierarchy is very similar in shape to the degree distribution, but that this property isn’t observed in existing random graph models. We additionally present methods to generate random graphs having density hierarchies similar to real networks. I will link to her thesis when it is finalized where this is covered in much more depth.
Theresa is looking forward to a future of teaching in institutes at higher education in countries of low-to-middle income. She’s an excellent teacher — far better than myself (though that may not be saying much) — and her future students will be lucky to learn from her.
Even though Theresa is delightful on an average day, I don’t think I’ve seen a smile as big as the one when she finished. Congratulations Dr. Migler-VonDollen!