Carnegie Mellon is a Destination for NSF Postdoctoral Fellows

The National Science Foundation (NSF) designates fewer than three dozen Mathematical Sciences Postdoctoral Research Fellowship annually. Two of the 2024 award recipients will conduct research at Carnegie Mellon University.

Sumun Iyer and Robert Krueger began postdoctoral research with faculty in Carnegie Mellon's Department of Mathematical Sciences this fall. Each fellowship supports a research and training project, under the mentorship of a sponsoring scientist.

Iyer, a Ph.D. graduate from Cornell University, studies logic and is mentored by Clinton Conley. Her project title is "Dynamics of Large Topological Groups."

"CMU has a really wonderful logic group, with lots of professors, postdocs and students, and, in my specific field of descriptive set theory, Clinton has a really wonderful group, as well," Iyer said.

Krueger, a Ph.D. graduate from University of Illinois, Urbana-Champaign, works in combinatorics and is mentored by Prasad Tetali. His project is titled "Extremal and Probabilistic Combinatorics."

"CMU has a number of professors who work in combinatorics, as well as postdocs who work in fields adjacent to mine, talented graduate students and very strong undergraduate students, and so, all around, I'm looking forward to collaborative experiences at CMU because those kinds of opportunities are what you want to gain from postdoctoral work," Krueger said.

Tetali, Alexander M. Knaster Professor and Department Head of Mathematical Sciences, has seen an increase in research awards to the department.

"It reflects well on the department because the MSPRF host institution must show an ability to provide the best next step in the career trajectory of a new Ph.D. graduate," Tetali said.

Previously, NSF awarded the MSPRF to Carnegie Mellon postdoctoral fellow Riley Thornton, sponsored by Conley, in 2022. The NSF also awarded an ASCEND fellowship to Carnegie Mellon postdoctoral fellow Aleyah Dawkins, sponsored by Michael Young, in 2023.

"For Clinton to receive sponsorship of two NSF postdocs [Iyer and Thornton] concurrently is truly impressive," Tetali said.

The Department of Mathematical Sciences also rose in rankings.

"The discrete math and combinatorics group in CMU-Math went up in the U.S. News and World Report rankings recently, from seventh to fourth in 2022, and then to third in 2023," Tetali said.

Krueger said he is influenced by Tetali's work, whose research focuses on probability theory, discrete mathematics and approximation algorithms. Tetali is a fellow of the American Association for the Advancement of Science, the American Mathematical Society and the Society for Industrial and Applied Mathematics.

"When Bob asked me to nominate him for the fellowship, it was an easy decision for me, as Bob's portfolio was very strong and the fit with CMU was also excellent," Tetali said.

Krueger's doctoral studies were advised by József Balogh, a researcher in extremal, additive, and probabilistic combinatorics. As an undergraduate student, he majored in math and physics with minors in computer science and statistics at Miami University of Ohio.

"Bob also has a background in computer science and statistics, both strong fields at CMU, so it was again an easy argument to makewhy we would be a great next step in Bob's academic journey," Tetali said.

Another opportunity ahead for Krueger is a 2025 spring program for researchers in extremal and probabilistic combinatorics at Simons Laufer Mathematical Sciences Institute. He will take a leave to complete the semester-long program in Berkeley, California.

"I'm excited the NSF fellowship allows me to pursue this opportunity as well," Krueger said.

For Iyer, her work in logic lies in the branch of descriptive set theory, as well as related branches such as model theory and topological dynamics. In addition to her Ph.D., she has a bachelor's degree in mathematics and English from Williams College.

Iyer's recent research is on non-locally compact topological groups.

"These are basically large spaces of symmetries that exhibit phenomena that smaller spaces of symmetries do not," Iyer said.

Her fellowship will allow her to continue this research, as well as branch out, she said.

Iyer became familiar with Conley's work while working on a joint question with another mathematician. They used Borel asymptotic dimension — a tool Conley has helped to develop.

"One exciting aspect of doing a postdoc is talking to people who are in your field but different enough from the work that you have already done that you can learn a lot and explore new ideas," Iyer said.

Conley's area of work sits at the intersection of set theory, dynamics and combinatorics.

"I was familiar with Sumun's work and invited her to speak at a seminar at CMU," he said. "She gave a beautiful talk, and I think she really will bring something unique to the department."

In addition to NSF postdoctoral fellows Iyer and Thornton, Conley advised Carnegie Mellon alumnus Felix Weilacher, who is a 2024 Ph.D. graduate of the Department of Mathematical Sciences and received a 2024 NSF MSPRF award. Weilacher began his postdoctoral research this fall at the University of California, Berkeley.

Past NSF MSPRF postdoctoral fellows at Carnegie Mellon have included Joshua Ballew, sponsored by Robert Pego; Amzi Jeffs, sponsored by Florian Frick; Robert Jerrard, sponsored by Mete Soner; and Michael Kowalczyk and Russell Schwab, both sponsored by David Kinderlehrer.

Conley said that the NSF postdoctoral fellows make important contributions to the department not only in research, but also teaching.

"Physics students, chemistry students, engineering students, and so on, all need to take math classes — so, there's a lot of teaching that needs to happen," Conley said. "University-level math is very central."