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Maroon Bells Wilderness Area

Undergraduate Research:

As an undergraduate, I twice had the opportunity to work with individual faculty members on research projects. Without these experiences I am not sure I would have become a mathematician. With them, I could not imagine doing anything else. My mentors were eager to hear my ideas and were patient when I struggled with new concepts. They were excited when we stumbled upon an interesting example or made a new insight. I look forward to providing undergraduates with similar experiences.

My research in Legendrian knot theory has complex geometric underpinnings. However, much of the complexity can be put aside and the theory can be reduced to combinatorics and algebra without losing computational power. The combinatorial and algebraic theory requires little more than multivariable calculus and linear algebra. Interesting examples are plentiful and easy to visualize and open questions are easy to pose. This area is ripe for undergraduate investigation and there is precedent for undergraduates contributing to current research.