Nick Salter enjoys making his own coffee, but he knows that coffee cups are more than just hot beverage receptacles. In fact, topologists like Salter, who joined the Department of Mathematics as an assistant professor in fall 2021, use coffee cups to explain the properties of surfaces and the numbers of holes in them.
(Fun fact: from a topological perspective, a coffee cup and a donut are the same shape, containing only one hole - see image below.)
Salter’s research combines topology, geometric group theory, and complex algebraic geometry to investigate surfaces and spaces. As he explained, “There are a lot of really subtle, deep questions still waiting to be answered about surfaces. The big questions are really about the way these things behave from the point of view of geometry.”
Salter appreciates the depth of topological knowledge in the department, so that he and other mathematicians can discuss each other’s work. “It was really nice to come here and suddenly have this ready-made group of colleagues, from the professors down to the graduate students, who are aware of what I’m doing,” Salter said.
Salter earned his bachelor’s degree in mathematics at Reed College in 2011, and his doctoral degree at the University of Chicago in 2017. He worked as a National Science Foundation mathematical sciences postdoctoral research fellow at Harvard University and Columbia University, before becoming a Ritt Assistant Professor at Columbia.
Salter’s undergraduate experience at a liberal arts college showed him how important it is for faculty to engage with their students, and he appreciates that the Notre Dame community shares this sentiment. “This balance between doing good research and being a good teacher [is] taken much more seriously here than it is at other places,” he said. “I found that refreshing, and I knew that I would have support and backing for things that I wanted to do that would involve teaching.”
In fall 2021, Salter taught a Calculus II course, and he will instruct a class on complex variables in spring 2022. He appreciates the level of organization in the Department of Mathematics. “It has really great infrastructure for teaching support, and I think it just leads to a lot better outcomes for students,” he explained.
Salter has always wanted to work at an institution with an engaged student body. He reflected that so far, his Notre Dame students have been very eager, hardworking, enthusiastic, and willing to learn, and he is excited to continue exploring mathematics with them. “You can’t ask for anything better than that,” he said.