# Graduating Doctoral Students 2016

Yue Cai is working in Algebraic Combinatorics with Professor Margaret Readdy. Her dissertation is "New Perspectives of Quantum Analogues"; see arXiv:1506.03249 [math.CO]. Her research focuses on new expressions for q-analogues and the algebraic and topological implications behind them. Recent talks include Princeton (May 2015) and Purdue (March 2016). She was the course assistant for the 2013 WAM Program at the Institute for Advanced Study and a MathExcel Instructor. She has been supported by the NSA and received the Wimberly Royster Teaching Assistant Award for excellence in research and teaching in 2014. Dr. Cai will begin a three year postdoc at Texas A&M in Fall 2016. |

Laura Croyle is working with Professor Russell Brown in the area of Partial Differential Equations. Croyle earned a Certificate in College Teaching and Learning and received a College of Arts and Sciences Certificate of Outstanding Teaching in 2014. She has also been active in outreach activities including Math Circles, an enrichment program for elementary and high school students, and STEM Camp, an enrichment program for middle school students. Croyle has also taught for the MathExcel program, which offers intensive workshops in collaborative problem-solving to help first-year students succeed in Calculus I and II. |

Neville Fogarty is working with Professor Heide Gluesing-Luerssen in algebraic coding theory. His research focuses on skew-constacyclic codes, which generalize cyclic codes by utilizing noncommutative skew-polynomial rings. Fogarty received a multi-year graduate fellowship and has a paper with Professor Gluesing-Luerssen in Finite Fields and Their Applications 35 (2015), 92-114 (see arXiv:1408.5445). He has been supported by the National Science Foundation, has taught with the MathExcel program and has been active in outreach activities including Elementary School Math Circles and High School Math Day. |

Shu Gu is working in Partial Differential Equations with Professor Zhongwei Shen. His dissertation is "Homogenization of Stokes Systems" and his research interest is regularity of solutions to elliptic boundary value problems. He has a joint paper with Professor Shen to appear in SIAM J. Math. Analysis (see also arXiv:1501.03392) and a single-author preprint on arXiv:1508.04203. Gu received the Wimberly Royster Teaching Assistant Award for excellence in research and teaching in 2014. |

John E. Mosley studies Algebraic Topology with Professor Serge Ochanine. His research focuses on finding a preferred class representative for SU-cobordism, and computing the image of SU-cobordism under the Witten genus. He has a single-author preprint in the area of number theory on arXiv:1411.0706. Mosley earned a Certificate in College Teaching and Learning in 2014. He has also been active in mathematics outreach including STEM Outreach Night at local middle schools, MPATE Day at Morehead State University, and volunteering as a tutor for a local STEM non-profit organization. |

Michael Music is working with Professor Peter Perry on inverse scattering theory and partial differential equations. His dissertation is "Global existence of solutions for the Novikov-Veselov Equation at zero energy." He has published papers in Inverse Problems 29 (4) (2013) (co-authored, arXiv:1211.3520), Inverse Problems and Imaging 8 (4) (2014), 1151-1167 (single-author, arXiv:1312.0567), and Contemp. Math.635, 25-70 (co-authored, arXiv:1312.5427), together with a joint paper, submitted to Commun. Math. Phys. on arXiv:1502.02632. Music has been supported by the National Science Foundation. |

Sarah Nelson is working with Professor Carl Lee in algebraic and geometric combinatorics, especially problems in enumerative combinatorics related to polytopes and winding numbers. Her dissertation is "Winding numbers, toric h-vectors, and CD-indices of convex polytopes." Nelson received the Wimberly Royster Teaching Assistant Award for excellence in teaching and research in 2015. She has also been active in outreach activities including Math Circles for elementary and high school students, High School Math Day for Women, and has taught with the MathExcel program. |

Yaowei Zhang is finishing his Ph.D. under the direction of Russell Brown. His general area of research is analysis and partial differential equations. He has extensive teaching experience including serving as primary instructor for an independent section of Calculus IV (Ordinary Differential Equations). His dissertation is on inverse boundary values for operators with non-smooth coefficients. He is interested in finding a non-academic job related to mathematics or statistics. |