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Brandy Guntel
Department of Mathematics 1 University Station C1200 Austin, TX 78712 Office: RLM 11.106 Email: bguntel (at) math utexas edu |
This Spring, I am teaching M408S: Integral Calculus for Science, M325K: Discrete Mathematics and M408L: Integral Calculus. For past semesters, click here. Research
My research lies in the area of exceptional Dehn surgeries, specifically Seifert fibered surgeries. A special class of knots, called primitive/Seifert knots, lie on the standard genus 2 Heegaard surface for the 3-sphere in such a way that guarantees surgery at the surface slope yields a Seifert fibered space or a connected sum of two lens spaces. (Though, by Eudave-Muñoz's thesis, the connected sum case only arises from surgery on a nonhyperbolic knot.) For my thesis, I considered questions of uniqueness for primitive/Seifert representatives of knots; I explored knots that are isotopic in the 3-sphere but not on the genus 2 surface. Now I am considering twisted torus knots that are fibered, as well as primitive/Seifert knots that admit L-space surgeries. Additionally, I am working on a project with John Berge and Sungmo Kang to classify primitive/Seifert knots, in the spirit of the primitive/primitive classification done by Berge. Click here to find my papers on the arXiv.