Neranga Fernando

Undergraduate Research Supervision

If you are interested in working on a research project with me, please send me an email or stop by my office so we can have a chat.

College of the Holy Cross, Worcester

  1. Zhaoqi Wu (current student)
    Research Topic: Quandles, racks and shelves
  2. Zhiyan Jiang (current student)
    Research Topic: A study of polynomials defined by functional equations and their applications in cryptography
  3. Thao Nghi Lam (current student)
    Research Topic: Applications of reversed Dickson polynomials in cryptography
  4. Sean Baker (current student)
    Research Topic: Self-reciprocal polynomials from Dickson polynomials and their applications in coding theory
  5. Qingjian (Jeston) Jiang (current student)
    Research Topic: Self-reciprocal polynomials from Dickson polynomials and their applications in coding theory
  6. Jiagi Fang
    Research Topic: Complete permutation polynomials arising from reversed Dickson polynomials
  7. Ming Wu
    Research Topic: Fixed points of reversed Dickson polynomials
  8. Jorge El Khoury
    Research Topic: Dickson polynomials and self-reciprocal polynomials
  9. Charlie Briley
    Research Topic: Dickson polynomials and self-reciprocal polynomials
  10. Melanie Lytle
    Research Topic: Dickson polynomials and self-reciprocal polynomials

Fall 2023 Research Associate Program Funded by J. D. Power Center at College of the Holy Cross

Reseacrh Associates: Jiagi Fang, Ming Wu

Topics Investigated:
  1. The interplay between quandles and codes
  2. Self-reciprocal polynomials and their applications in coding theory

Weiss Summer Science Research Program from June 5, 2023 to July 28, 2023 at College of the Holy Cross

Students supervised: Jiagi Fang, Ming Wu

Research Topics:
  1. Cycle types of reversed Dickson permutation polynomials
  2. Fixed points of reversed Dickson permutation polynomials
  3. Complete permutation polynomials arising from reversed Dickson polynomials
  4. Quandles, Shelves, Racks
  5. Partially Ordered Sets
  6. Lotka-Volterra equations
  7. Operations research
Research Articles: Reversed Dickson polynomials. Accepted in Involve arXiv

Dissemination of Results: The results of the Weiss program were/will be presented by Jiaqi Fang and Haoming Wu at
  1. Weiss Summer Research Symposium at College of the Holy Cross, September 8, 2023,
  2. AMS sectional meeting at the University of South Alabama, October 13 -- 15, 2023, and
  3. Academic Conference at College of the Holy Cross, April 24, 2024.
Here are the posters of Ming and Jiaqi at Weiss Summer Research Symposium at College of the Holy Cross held on September 8, 2023: Ming, Jiaqi

Northeastern University, Boston

  1. Noah Lichtblau
    Research Topic: Fibonacci Numbers and Zumkeller Numbers. Noah pointed out that the 18th Fibonacci number, 2584, is a Zumkeller number. The divisors of 2584 are 1, 2, 4, 8, 17, 19, 34, 38, 68, 76, 136, 152, 323, 646, 1292, 2584. They can be split into {2, 4, 34, 76, 2584} and the rest, each having a sum of 2700.
  2. Walker Miller-Breetz
    Research Topic: Polynomial gn,q.
  3. Jackson Steilberg
    Research Topic: Functional graphs.
  4. Yuval Timen
    Research Topic: Quandles.
  5. Aliya Tyshkanbayeva
    Research Topic: Lucas polynomials.
  6. Mohammad H. Rashid
    Research Topics: Permutation polynomials over finite fields, Self-reciprocal polynomials, Fibonacci polynomials, Partitions.
    Research Articles: Fibonacci self-reciprocal polynomials and Fibonacci permutation polynomials (Submitted for publication)
  7. Honors Project: Siddhartha Pant (Spring 2016)
    Research Topic: Dickson polynomials over finite fields.
  8. Luke Kyungmin Shin (Fall 2014 & Spring 2015)
    Research Topic: Permutation polynomials over finite fields.

University of South Florida, Tampa

  1. I was the Mathematics Advisor for two undergraduate projects in Engineering Calculus at the University of South Florida:

    - Projectile Motion of Missiles

    - Tangencies of the Efficient Frontier and Individual Utility



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