Fernando Roman, Ph.D.
Education: Bachelor of Science in mathematics (May 2015)
Master of Science and Doctor of Philosophy in mathematics from the University of Illinois Urbana-Champaign
McNair Project: Exceptional Surgeries on Montesinos Knots (2013)
Mentor: David Auckly, Ph.D.
Exceptional surgeries on Montesinos knots have been extensively studied in the last few years. Such surgeries have been completely classified with the exception of Seifert fibred surgeries on Montesinos Knots of length 3. A list of surgeries yielding small Seifert fibred spaces was provided by Wu, together with a conjecture that the list is complete. In this expository paper we introduce some basic concepts in knot and Dehn surgery theory, and discuss Seifert fibred surgeries on Montesinos knots. We look at a specific family of knots and try to determine which surgeries on this knots yield a small Seifert fibre space.