


Hannah Larson
$50,000 Scholarship Recipient
Age: 18 Eugene, OR Category: Mathematics Project Title: “Classification of Some Fusion Categories of Rank 4”______ _______ ________ ____ _______ 


Fusion categories are fundamental mathematical objects that appear in many areas of math, physics, and computer science. The classification of fusion categories is a difficult, open problem of current interest in mathematics. Hannah's project makes progress towards solving this problem by studying the next unsolved case of smallest rank. One way to approach the classification of fusion categories is to study related objects called fusion rings and determine which fusion rings can be associated with fusion categories. This is an open problem that has only been answered when the fusion rings have 1, 2, or 3 basis elements. Hannah considers fusion rings with 4 basis elements. Out of a large number of existing fusion rings, Hannah proves that very few can be associated with fusion categories. Using these fusion rings, one may be able to construct new fusion categories which will improve our understanding, and may lead to progress in physics and computer science.
Hannah hopes that her research will contribute to the body of mathematical knowledge, which is important for progress in the other sciences. She believes that fundamental research in the sciences can have a great impact on the world. Fusion categories have potential applications in theoretical physics and quantum computation.
Hannah attends Harvard College and plans to major in mathematics. Hannah won fourth place at the 2013 Intel Science Talent Search as well as fourth at the 2013 Intel Science and Engineering Fair. She won second place in this year’s Karl Menger Award given by the American Mathematical Society. Aside from math, Hannah is an avid cello player and founded a string quartet. She enjoys running, swimming and playing soccer.
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