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.” Anna Romanova
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
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