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

Mathematics Honors Thesis Supervised

1. Zhaoqi (Zack) Wu (Fall 2024 and Spring 2025)
   Thesis Titlte: A Study of Knots and Quandles

Fall 2024 Research Associate Program Funded by J. D. Power Center at College of the Holy Cross

1. Quandle rings and shelf rings
2. Gröbner bases and their applications in Quandle rings
3. Self-reciprocal polynomials and Dickson polynomials of the (k + 1)th kind
4. Complete permutation polynomials defined by functional equations and their applications in Cryptography.

1. Weiss Summer Research Symposium at College of the Holy Cross, September 6, 2024,
2. A seminar in the Department of Mathematics and Computer Science at College of the Holy Cross in Fall 2024,
3. A math conference at Smith College on September 21, 2024, and
4. Academic Conference at College of the Holy Cross, April 23, 2025.

Weiss Summer Science Research Program from June 3, 2024 to July 26, 2024 at College of the Holy Cross

1. Quandles, racks and shelves
2. Polynomials defined by functional equations and their applications in cryptography
3. Self-reciprocal polynomials from Dickson polynomials and their applications in coding theory

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

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

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

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.

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 g_n,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