The Secret World of Math

Anna Romanova

The Secret World of Math

Anna Romanova, who will receive a Ph.D. in mathematics in May, always enjoyed math classes in her early school years, but admits that she didn’t really understand what math was until late in her senior year of college. She took a point set topology class where the goal was to classify all compact topological surfaces. Instead of just stating the theorem and proving it, her professor guided the class through a process of “discovery,” whereby the students figured out what the answer had to be and then constructed the proof together. “This was the first time that math had felt like an exploration,” said Romanova, “and it was incredibly appealing to me. This is still what appeals to me about math—doing math feels like I’m uncovering a secret world. And representation theory is an especially beautiful world to uncover—it’s full of patterns and surprising connections with other fields of math.”

Research and Teaching

In doing research, Romanova classifies herself as being under the umbrella of “geometric representation theory,” which means that she looks at representation theory problems using tools from geometry. In studying the representation theory of Lie groups, she borrows tools from algebraic geometry. By using a technique that mathematicians developed in the early 1980s, it’s possible to translate questions about representation theory of Lie groups into questions about differential equations. “These differential equations live on certain nice geometric shapes called varieties,” said Romanova. “The power in this translation is that it allows us to use a whole new set of tools developed by algebraic geometers to tackle our representation theory problems, and often these tools are more effective.”

In addition to her research, Romanova has taught a wide range of undergraduate courses at the U, including college algebra, pre-calculus, linear algebra, and discrete math. She recently taught a class on representation theory techniques in quantum physics. “Like most things, math is much more satisfying when you can share the experience, and this is how I see my role as a teacher,” she said. “I am there to share the delight of learning new math with my students and to guide them through the process so that it can be a positive and enriching experience for all of them.”

Raised in northern Nevada, she received two bachelor’s degrees from Colorado State University. She obtained a Bachelor of Science in mathematics and a Bachelor of Arts in

Spanish language, literature, and culture. For the past six years, she has worked with Dragan Miličić, professor of mathematics, at the U. “I feel so lucky to have had the opportunity to work with Dragan,” she said. “He has generously shared his wealth of mathematical knowledge with me. Learning about his perspective on representation theory and watching his intuition with problems has been a very valuable experience.”

Diversity and Inclusion

Romanova feels strongly about the fact that certain groups are underrepresented within mathematics. “I find the contrast between the homogeneity of most math departments and the diversity of our country (and world) to be deeply disturbing. On one hand, this means that we are missing out on all of the ideas that these missing people could contribute to mathematics. But more importantly, it seems to reflect the power imbalance of our country, where only certain people have access to the social benefits of higher education. These issues are complicated and unlikely to be solved anytime soon, but I think that talking about them is an important first step.” While at the U, Romanova has been involved in the Association for Women in Mathematics (AWM).

Recently, Romanova was awarded a National Science Foundation postdoctoral research fellowship to work with Professor Geordie Williamson at the University of Sydney. In addition, she received the “Best Graduate Student Research Poster” award for the AWM’s poster competition at the Joint Mathematics meetings held in San Diego in January.

Following graduation, Romanova will relocate to work at the University of Sydney in Australia.