Applied Studies: Tikhomirov Approaches Probability with an Engineer’s Mindset

As a child, Konstantin Tikhomirov couldn't wait for the school math competitions, where he'd happily spend hours solving math puzzles. He pursued his interests in applied math and information technology as an undergraduate student at Samara State University in Russia with thoughts of possibly becoming a professor. But finding an academic position in Russia was difficult, so he switched his career aspiration to something that seemed more realistic — software engineering. Upon graduation, he took a job as a software engineer. But something was missing.

"I realized that there are truly gifted software engineers who set up companies and create beautiful products. I felt that my personality is not of that type. Whereas in math, I've always had feelings that I can do much more," said Tikhomirov, an associate professor of mathematical sciences.

Tikhomirov started taking graduate courses in math while working part-time at a software company. He earned a candidate of sciences degree in Pure Mathematics at Samara State University and his Ph.D. from the University of Alberta, Canada. Between his undergraduate degree in applied math and his software engineering job, Tikhomirov lost touch with his long-standing interest in pure math questions. During his doctoral work, he found himself back in familiar territory.

"I was attracted to beautiful proofs, aesthetically pleasing statements with no real sort of applications," he said. But then he began working on questions in probability, and things started to shift.

"I would say now, when I work on a question, I have in mind this applied perspective," he said. "It doesn't mean I see the engineering applications of my work, but I hope that a method that I develop along the way can be useful in some applied context."

Much of Tikhomirov's research has focused on asymptotic geometric analysis, random matrices, probability theory and convex geometry. He recently started to work on topics in probabilistic combinatorics — a hybrid of probability and combinatorics, where the main object of study is probability distributions on discrete structures. Tikhomirov is especially interested in questions related to random graphs, including graph matching.

Tikhomirov's career has taken him to many different places — Russia, Canada, Princeton, Berkeley, Atlanta — and he is excited to call Pittsburgh home.

"Carnegie Mellon's math department is famous for several directions, especially combinatorics and probabilistic combinatorics," Tikhomirov said. "In that respect, the department is perfect for my research interests."