Jie L. Liang, '12
Jie Liang moved to the United States from China after she finished high school. To further her education, she attends University of Central Florida majoring in mathematics as a first generation undergraduate. Because of her dedication to obtaining a Ph.D. degree in mathematics, she seeks research opportunities. In 2010, Jie participated in a year-long research project named GAUSS in UCF funded by NSF. She worked under Dr. Xin Li on applying reweighed least square method to face recognition and submitted their paper to Undergraduate Research Journal. In summer 2011, Jie conducted research with Dr. Garvan at University of Florida on number theory through the Summer Research Experience for Rising Senior program. Together with Dr. Andrews from Pennsylvania State University, they submitted their paper to Ramanujan Journal. As a senior, Jie is currently working on her Honors in the Major thesis with Dr. Li on approximation theory.
Ph.D. in Mathematics
Combinatorial Interpretations of Congruences for the SPT-Function Conducted at University of Florida as part of the Summer Research Experience for Rising Seniors program in the summer of 2011 Mentor: Dr. Frank Garvan. Math Department, University of Florida Participants: Jie Liang Authors: G. Andrews, F. Garvan, and J. Liang Abstract: Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. In 1988, the second author gave new combinatorial interpretations of Ramanujan's partition congruences mod 5, 7 and 11 in terms of a crank for weighted vector partitions. In 2008, the first author found Ramanujan-type congruences for the spt-function mod 5, 7 and 13. We give new combinatorial interpretations of the spt-congruences mod 5 and 7. These are in terms of the same crank but for a restricted set of vector partitions. The proof depends on relating the spt-crank with the crank of vector partitions and the Dyson rank of ordinary partitions. We derive a number of identities for spt-crank modulo 5 and 7. We prove the surprising result that all the spt-crank coefficients are nonnegative.
Summer Research Institution
University of Florida
University of Florida (Ph.D.)
Liang, Jie L., "Jie L. Liang, '12" (2017). McNair Scholars. 61.