A Q&A with Hannah Larson, a recipient of the 2024 Maryam Mirzakhani New Frontiers Prize
Hannah Larson is obsessed with understanding what happens when two or more mathematical objects intersect. Larson, a mathematician at the University of California, Berkeley, and a research fellow at the Clay Mathematics Institute, recently won a 2024 Maryam Mirzakhani New Frontiers Prize. It’s named after the first female mathematician to win the Fields Medal, often described as the Nobel Prize of math.
While Larson was an undergraduate student at Harvard University, she became captivated by the mathematics she was learning in an intersection theory class. “I thought that course was so amazing, and the things you could calculate using intersection theory were so cool,” Larson says. Furthermore, if I trace out a path within the moduli space, that corresponds to a continuously varying family of our objects. What that means is a little difficult to make precise, but we can take this example: the moduli space of circles. Every circle is determined by its center, , and its radius, r. So the moduli space of circles is a three-dimensional space of triples, , where r is greater than zero.
Another one is finding maps between spaces. If you’re trying to understand one moduli space, and you can map that moduli space to a simpler one, you can often use your understanding from the simpler moduli space to say something about the more complicated one. Giving a map from one moduli space to another is like a rule for taking objects of one type and getting objects of a different—hopefully simpler—type.
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