Neranga Fernando

Department of Mathematics
Knox College
2 E South St
Galesburg, IL 61401
United States
Email: nfernando AT knox DOT edu
Office Phone: 309-341-7520

I am a Visiting Assistant Professor in the Department of Mathematics at Knox College in Galesburg, Illinois.

I was born in Negombo in Sri Lanka and raised in Ekala, which is a small town in the west coast of Sri Lanka. I completed my elementary education at Newstead Girls College in Negombo (the oldest existing girls’ college in Sri Lanka), and then went to Maris Stella College in Negombo to complete my middle school education and high school education. Having earned my B.Sc. (special) degree in Mathematics at the University of Kelaniya in Sri Lanka, I moved to Florida to complete my Master’s degree and Doctoral degree in Mathematics at the University of South Florida . I completed my Ph.D. in Spring 2013 at the University of South Florida under the supervision of Professor Xiang-dong Hou with a dissertation titled A study of permutation polynom ials over finite fields. I moved to Boston in August, 2013 to be a Lecturer (this designation was renamed as Assistant Teaching Professor in 2018) in the Department of Mathematics at Northeastern University, and I was there until June, 2019. In July 2019, I moved to Pittsburgh to join Carnegie Mellon University for a year. In July 2021, I moved to Worcester to join the Department of Mathematics and Computer Science at College of the Holy Cross as a Visiting Assistant Professor. In August 2025, I joined the Department of Mathematics at Knox College in Galesburg, Illinois.

Academic Experience

Visiting Assistant Professor, Knox College, Galesburg, IL, 09/2025 - Present
Visiting Assistant Professor, College of the Holy Cross, Worcester, MA, 08/2021 - 08/2025
Eugene P. Shelly Visiting Assistant Professor, Carnegie Mellon University, Pittsburgh, PA, 08/2019 - 05/2020
Lecturer/ Assistant Teaching Professor, Northeastern University, Boston, MA, 08/2013 - 06/2019
Graduate Teaching Assistant, University of South Florida, Tampa, FL, 01/2008 - 05/2013
Teaching Assistant, University of Kelaniya, Kelaniya, Sri Lanka, 05/2007 - 12/2007

Research Interests

1. Finite Fields and Their Applications

 - Permutation polynomials over finite fields 
 - Self-reciprocal polynomials and their applications in  coding theory. 
 - Complete mappings over finite fields and their applications in cryptography. 
 - Irreducible polynomials over finite fields
 - Dickson polynomials, reversed Dickson polynomials, and polynomials defined by functional equations over finite fields.

2. Quandle Theory

 - Quandles, racks, shelves, and their applications in knot theory.

3. Quandle Rings and Their Applications in Knot Theory

4. Elementary Number Theory

5. Computational Number Theory

6. Experimental Mathematics

Publications

(with G. Churchill, I. R. Churchill, B. Kousik) A further study of quandles and quandle rings. arXiv
(with B. Kousik) A further study of polynomial g_n,q over finite fields. arXiv
Reversed Dickson polynomials of the (k+1)-th kind over finite fields, II. Contributions to Discrete Mathematics, Volume 20, Issue 2, 2025, 1 – 29. journal arXiv
(with M. Elhamdadi and M. P. Goonewardena) Classification of connected shelves. New Zealand J. Math. 56 (2025), 53 - 68. journal arXiv
(with J. Fang and H. Wu) Reversed Dickson polynomials. Involve, a Journal of Mathematics 18-2 (2025), 297 - 328. journal arXiv
(with S. U. Hasan and M. Pal) Dembowski-Ostrom polynomials and Reversed Dickson polynomials. Discrete Applied Mathematics (2021) journal arXiv
(with M. Elhamdadi and B. Tsvelikhovskiy) Ring theoretic aspects of quandles. Journal of Algebra (2019) journal arXiv
A note on the permutation behaviour of the polynomial g_n,q. INTEGERS: The Electronic Journal of Combinatorial Number Theory 19 (2019). journal arXiv
(with S. Manukure) A note on Dickson polynomials of the third kind and Legendre functions. Journal of Inequalities and Special Functions (2019) journal arXiv
A note on permutation binomials and trinomials over finite fields. New Zealand J. Math. 48 (2018), 25-29. journal arXiv
(with I. R. Churchill and M. Elhamdadi) The cocycle structure of the Alexander f-quandles on finite fields. J. Algebra Appl. 17 (2018) journal arXiv
Self-reciprocal polynomials and coterm polynomials. Des. Codes Cryptogr. 86 (2018), no. 8, 1707-1726. journal arXiv
Note: In Theorem 2.3, it must be ‘‘Let n > 4 be even’’. In Theorem 2.6, it must be ‘‘Let n > 5 be odd’’
Reversed Dickson polynomials of the (k+1)-th kind over finite fields. J. Number Theory 172 (2017), 234-255.journal arXiv
Reversed Dickson polynomials of the third kind. In: Gloria Scientiam. University of Kelaniya, Sri Lanka (2017), Chapter 50: 585-598. journal arXiv
(with X. Hou) From r-linearized polynomial equations to r^m-linearized polynomial equations. Finite Fields Appl. 37 (2016), 14-27. journal arXiv
(with X. Hou and S. D. Lappano) Permutation polynomials over finite fields involving x+x^q+…+x^{q^a-1}. Discrete Math. 315 - 316 (2014), 173-184. journal
(with X. Hou and S. D. Lappano) A new approach to permutation polynomials over finite fields, II. Finite Fields Appl. 22 (2013), 122-158. journal arXiv
(with X. Hou) A piecewise construction of permutation polynomials over finite fields. Finite Fields Appl. 18 (2012), 1184-1194. journal

Ph.D. Thesis

A study of permutation polynomials over finite fields. Ph.D. Dissertation, University of South Florida, Tampa, FL, USA (2013). Ph.D. Thesis

Unrefereed Publications

(with M. H. Rashid) Fibonacci self-reciprocal polynomials and Fibonacci permutation polynomials. arXiv
Dembowski-Ostrom polynomials and reversed Dickson polynomials. arXiv

Coauthors

Gregory Churchill (SUNY at Oswego, USA)
Indu Rasika Churchill (SUNY at Oswego, USA)
Mohamed Elhamdadi (USF, Tampa, USA)
Jiaqi Fang^* (College of the Holy Cross, USA)
Matthew Goonewardena (Ericsson, Montreal, Canada)
Sartaj Ul Hasan (IIT Jammu, India)
Xiang-dong Hou (USF, Tampa, USA)
Bhitali Kousik ^** (Tezpur University, Assam, India)
Stephen D. Lappano (USF, Tampa, USA)
Solomon Manukure (Florida A&M University, USA)
Mohit Pal (Indian Statistical Institute, Kolkata)
Mohammad H. Rashid^* (Northeastern University, Boston, USA)
Boris Tsvelikhovskiy (University of California Riverside, USA)
Haoming Wu^* (College of the Holy Cross, USA)

^* denotes an undergraduate student.
^** denotes a graduate student.

Talks

Permutation polynomials, local permutation polynomials, and polynomial g_{n,q}, 17th International Conference on Finite Fields and their Applications Fq17, June 14 - 18, 2027, University College Dublin, Ireland. (abstract to be submitted)
(invited) Permutation polynomials over finite fields, their applications, and undergraduate research projects , Faculty Seminar, Knox College, November 13, 2026.
(invited) Zero divisor graphs of quandle rings , Special Session on Algebraic Methods in Graph Theory and Applications, Joint Mathematics Meetings, Chicago, January 12 - 15, 2027.
(invited) Quandle rings and their applications in coding theory , Special Session on Coding Theory and Applications, AMS Sectional Meeting, University of Minnesota Duluth, MN, October 24-25, 2026.
Answers to Open Questions on Quandles and Quandle Rings, and an Introduction to Zero-Divisor Graphs of Quandle Rings, Special Session on Knots and Braids, AMS Sectional Meeting, George Washington University, Washington D.C., October 2 - 3.
Zero-divisor Graphs of Quandle Rings , Midwest Combinatorics and Graph Theory Conference at Miami University, Oxford, Ohio, September 18 - 19.
Contributions to the family of reversed Dickson polynomials , Combinatorial and Additive Number Theory (CANT 2026) Conference, New York Number Theory Seminar, July 13 - July 17, 2026. Video
Reversed Dickson polynomnials over fintie fields , International Workshop on the Arithmetic of Finite Fields WAIFI 2026, Santander, Spain. June 3 - 5, 2026.
Quandle rings and their applications in coding theory , International Workshop on the Arithmetic of Finite Fields WAIFI 2026, Santander, Spain. June 3 - 5, 2026.
Permutation polynomials and local permutation polynomials over finite fields defined by functional equations , Special Session on Finite Fields and Their Applications, AMS Sectional Meeting, Boston College, MA, March 28 - 29, 2026.
(invited) Quandle rings and open problems for undergraduate students , Mathematics Seminar, Department of Mathematics, State University of New York at Oswego, March 3, 2026.
(invited) Permutation polynomials and reversed Dickson polynomials , Mathematics Seminar, Department of Mathematics, State University of New York at Oswego, October 14, 2025
Idempotents in quandle rings , Special Session on Nonassociative Algebraic Structures, AMS Sectional Meeting, University of Denver, Denver, CO, August 23 - 24, 2025.
(invited) Reversed Dickson polynomials over finite fields , Special Session on Number theory at Primarily Undergraduate Institutions, AMS Sectional Meeting, California Polytechnic, San Luis Obispo, CA, May 3 - 4, 2025.
Permutation polynomials and reversed Dickson polynomials , Rose-Hulman Institute of Technology, Terre Haute, IN, April 25, 2025.
Idempotents and tripotents in quandle rings , Knots in Washington, George Washington University, December 6 - 8, 2024.
(invited) Idempotents and tripotents in Quandle Rings , Scientific Session on Finite Fields and Their Applications, Canadian Mathematical Society Winter Meeting 2024, Vancouver, Canada, November 29 - December 2, 2024.
Idempotents in quandle rings , Special Session on Invariants of Knots, Links, and Low-dimensional Manifolds, AMS Sectional Meeting, University of Albany, Albany, New York, NY, October 19 - 20, 2024.
Quandles, racks and shelves , Clavius Group Meeting, College of the Holy Cross, Worcester, MA, June 22, 2023.
Reversed Dickson polynomials of the (k+1)-th kind over fintie fields , Clavius Group Meeting, College of the Holy Cross, Worcester, MA, June 20, 2023.
Reversed Dickson polynomials of the (k+1)-th kind over fintie fields , Scientific Session on Finite Fields and Their Applications, Canadian Mathematical Society Summer Meeting 2023, Ottawa, Canada, June 4, 2023.
Classification of connected shelves and their applications to positive knots , Claremont Topology Seminar, Claremont Center for the Mathematical Sciences, Claremont, CA, March 7, 2023.
(invited) Knots, quandles and shelves , Discrete Mathematics Seminar, Worcester Polytechnic University, Worcester, MA, February 20, 2022.
(invited) Quandles, racks and shelves and their applications to positive knots , Purdue University, West Lafayette, IN, February 7, 2023.
Quandles, racks and shelves , School of Mathematics and Statistics, Carleton University, Ottawa, Canada, October 14, 2022.
(invited) Self-reciprocal polynomials and reversed Dickson polynomials , Mathematics Colloquium, University of South Florida, Tampa, FL, March 11, 2022.
Self-reciprocal polynomials arising from reversed Dickson polynomials , College of the Holy Cross, Worcester, MA, February 9, 2022.
Permutation polynomials over finite fields , College of the Holy Cross, Worcester, MA, November 3, 2021.
Sel-reciprocal polynomials and reversed Dickson polynomials , Rose-Hulman Institute of Technology, Terre Haute, IN, May 6, 2021.
. Self-reciprocal polynomials and Zumkeller numbers , Amherst College, Amherst, MA, March 4, 2019.
Fibonacci permutation polynomials , Math Club, California State University, Northridge, CA, March, March 9, 2018.
Reversed Dickson permutation polynomials , Algebra, Number Theory, and Discrete Mathematics Seminar, California State University, Northridge, CA, March 7, 2018.
Reversed Dickson permutation polynomials over finite fields , Algebra, Number Theory, and Combinatorics Seminar, Claremont Center for the Mathematical Sciences, Claremont, CA, March 6, 2018.
Self-reciprocal polynomials arising from reversed Dickson polynomials , Special Session on Polynomials in Enumerative, Algebraic, and Geometric Combinatorics, AMS Sectional Meeting, State University of New York at Buffalo, Buffalo, NY, September 16 - 17, 2017.
Reversed Dickson polynomials of the (k+1)-th kind over finite fields, II , Special Session on Numbers, Functions, Transcendence, and Geometry, AMS Sectional Meeting, University of North Texas, Denton, TX, September 9 - 10, 2017.
(invited) Reversed Dickson polynomials of the (k+1)-th kind over finite fields , Special Session on Finite Fields and their Applications, AMS Sectional Meeting, Hunter College, CUNY, New York, NY, May 6 - 7, 2017.
A generalization of the reversed Dickson polynomials over finite fields , Discrete Mathematics Seminar, University of South Florida, March 6, 2017.
(invited) Permutation polynomials, self-reciprocal polynomials, and their role in coding theory , Northeastern University, December 1, 2016. (Chalkboard presentation)
(invited) Reversed Dickson polynomials of the third kind , 47th Southeastern International Conference on Combinatorics, Graph Theory & Computing, March 7-11, 2016.
(invited) From r-linearized polynomial equations to r^m-linearized polynomial equations , Fq12: The 12th International Conference on Finite Fields and Their Applications, Saratoga Springs, NY, July 13-17, 2015.
New classes of permutation polynomials over finite fields defined by functional equations , Joint Mathematics Meeting , San Diego, Jan 9 - 12, 2013.
A New Approach to Permutation Polynomials over Finite Fields , Discrete Mathematics Seminar, University of South Florida, November 19, 2012.
(invited) Permutation Polynomials over Finite Fields defined by functional equations , AMS Sectional Meeting, University of South Florida , March 10-11, 2012.
A Matrix form of the Jacobi-Trudi Identity , Discrete Mathematics Seminar, University of South Florida, February 8, 2010.

Conference Organization

Organizer of the special session on finite fields and their applications at AMS Sectional Meeting at Boston College, March 28 - 29, 2026. https://www.ams.org/meetings/sectional/2331_program_ss12.html#title

I gratefully acknowledge financial support to the session on finite fields and their applications from the Journal of Number Theory (Elsevier).
Co-organizer of the special session on quandles and quandle rings at Spring Western Virtual AMS Sectional Meeting, April 3 - 4, 2027.

Research Visits and Workshops

Workshop on Research experiences for undergraduate faculty, Richard N. Merkin Center for Pure and Applied Mathematics, The American Institute of Mathematics, California Institute of Technology, Pasadena, CA, July 27 - 31, 2026.
A research visit to California State University, Northridge, August 10 - 16, 2025. Host: Daniel J. Katz

Description for screen readers — With Daniel in Malibu

Upcoming Conferences and Workshops

Special Session on Algebraic Methods in Graph Theory and Applications, Joint Mathematics Meetings, Chicago, January 12 - 15, 2027.
Spring Western Virtual AMS Sectional Meeting, April 3 - 4, 2027.
17th International Conference on Finite Fields and their Applications Fq17, June 14 - 18, 2027, University College Dublin, Ireland.

Teaching Experience

Knox College, Galesburg, IL

Calculus 1 MATH 145
Number Theory MATH 217
Linear Algebra MATH 185
Real Analysis MATH 331 (Spring 2027)
Discrete Mathematics MATH 175
Calculus 3 MATH 205
Introductory Statistics STAT 200
Research in Mathematics MATH 361
Topics in Operations Research - Independent Study
Topics in Coding Theory - Independent Study (Winter 2027)

College of the Holy Cross, Worcester, Massachusetts, USA

Calculus 1 with Fundamentals MATH 133
Calculus 1 MATH 135
Calculus 2 MATH 136
Categorical Data Analysis STAT 232
Multivariable Calculus MATH 241
Mathematical Structures MATH 243
Linear Algebra MATH 244
Modern Algebra MATH 351
Real Analysis MATH 361
Probability Theory STAT 375
Topics in Coding Theory MATH 400 (Directed Reading)
Representation Theory MATH 400 (Directed Reading)
Field and Galois Theory MATH 410 (Directed Project)
Topics in Finite Fields MATH 410 (Directed Project)
Polynomials over Finite Fields MATH 410 (Directed Project)
Knot Theory and Quandle Theory MATH 495 (Mathematics Honors Thesis)
Knot Theory and Quandle Theory MATH 496 (Mathematics Honors Thesis)

Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

21-120 Differential and Integral Calculus
21-259 Calculus in Three Dimensions
21-240 Matrix Algebra with Applications

Northeastern University, Boston, Massachusetts, USA

Calculus and Differential Equations for Biology II MATH 1252
Calculus 1 for Science and Engineering MATH 1341 (Honors)
Calculus 1 for Science and Engineering MATH 1341
Calculus 2 for Science and Engineering MATH 1342
Calculus 3 for Science and Engineering MATH 2321 (Honors)
Calculus 3 for Science and Engineering MATH 2321
Differential Equations and Linear Algebra for Science and Engineering MATH 2341
Discrete Mathematics MATH 2310
Linear Algebra MATH 2331
Probability and Statistics MATH 3081
Group Theory MATH 3175
Number Theory I MATH 3527
Combinatorial Mathematics MATH 3533
Number Theory II MATH 4527
Advanced Linear Algebra MATH 4571
Topics in Finite Fields MATH 4993 (Independent Study)
Dickson Polynomials over Finite Fields MATH 4970 (Directed Research Study)

University of South Florida, Tampa, Florida, USA (As a graduate student)

Finite Mathematics MGF 1106 (Instructor of Record) - Fall 2011 and Fall 2012
Engineering Calculus 1 MAC 2281 (Instructor of Record) - Fall 2010

Mathematics Honors Thesis Supervision

College of the Holy Cross, Worcester, MA

Student: Zhaoqi (Zack) Wu

Thesis Title: A Study of Knots and Quandles (Fall 2024 & Spring 2025)

Zack successfully defended his thesis on May 7, 2025.

He also presented sections 9, 10 & 11 of his thesis, which contain original results, at an undergraduate math conference at Union College in Schenectady in New York on April 5, 2025.

Zack’s honors thesis can be accessed through the following link:

https://crossworks.holycross.edu/math_honor/64/

Current Position: Graduate student at the University of Pennsylvania

Academic Advising

I am currently the academic advisor for a student at Knox College who is majoring in mathematics and physics. I have also advised students in academic matters at my previous institutions, although not in an official capacity.

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.

Knox College, Galesburg, IL

Upasana Aryal (current student)
Research Topic: Reversed Dickson polynomials and differential equations
Sy Quoc Uy Vo (Herry) (current student)
Research Topic: Classifying self-reciprocal polynomials from Dickson polynomials
Tan Le
Research Topic: Analyzing the distributions of value sets of reversed Dickson polynomials
Aaditya Trivedee
Research Topic: Intergenerational mobility
Tam Nguyen (Katie)
Research Topic: Foxes vs Rabbits in Illinois - a predator-prey model

Dissemination of Results: Tan Le, Herry Vo and Katie Nguyen presented their research results at an undergraduate mathematics conference at Rose-Hulman Institute of Technology in Terre Haute, Indiana on March 28, 2026.

College of the Holy Cross, Worcester

Zhiyan (Jack) Jiang (current student)
Research Topic: A study of polynomials defined by functional equations and their applications in cryptography
Current Position: Graduate Student at Worcester Polytechnic University
Zhaoqi (Zack) Wu (High Honours)
Research Topic: Quandles, racks and shelves
Current Position: Graduate Student at the University of Pennsylvania
Qingjian (Jeston) Jiang
Research Topic: Permutation polynomials defined by functional equations over finite rings, cycle types of permutation polynomials over finite fields
Current Position: Graduate student at the University of Southern California
Sean Baker
Research Topic: Self-reciprocal polynomials from Dickson polynomials and their applications in coding theory
Jiagi Fang (Honours)
Research Topic: Complete permutation polynomials arising from reversed Dickson polynomials
Current Position: Graduate Student at Columbia University
Ming Wu
Research Topic: Fixed points of reversed Dickson polynomials
Current Position: Graduate Student at Columbia University
Jorge El Khoury
Research Topic: Dickson polynomials and self-reciprocal polynomials
Charlie Briley
Research Topic: Dickson polynomials and self-reciprocal polynomials
Melanie Lytle
Research Topic: Dickson polynomials and self-reciprocal polynomials

Spring 2025 Research Associates Program Funded by J.D. Power Center at College of the Holy Cross

Research Associates: Qinjian (Jeston) Jiang

Topics investigated:

 * Permutation polynomials defined by functional equations over finite rings.

Dissemination of Results:

Jeston presented the results of his research project at 
1. An undergraduate math conference at Union College on April 5, 2025, and 
2. Academic Conference at College of the Holy Cross, April 23, 2025. 

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

Research Associates: Sean Baker, Zhaoqi (Zack) Wu , Zhiyan (Jack) Jiang

Topics investigated:

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

Dissemination of Results:

Sean, Zack and Jack presented their research results at a student research seminar in the Department of Mathematics and Computer Science at College of the Holy Cross in Fall 2024 and Spring 2025.

Zack and Jack also presented their research results at

An undergraduate math conference at Smith College on September 21, 2024, and
Academic Conference at College of the Holy Cross on April 23, 2025.

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

Students supervised: Zhaoqi (Zack) Wu, Zhiyan (Jack) Jiang, Sean Baker

Topics Investigated:

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

Sean, Zack and Jack presented their research results at the Weiss Summer Research Symposium at College of the Holy Cross, which was held on September 6, 2024. Their posters can be accessed via the following links:

https://mathcs.holycross.edu/~nfernand/Posters/Sean.pdf
https://mathcs.holycross.edu/~nfernand/Posters/Zack.pdf
https://mathcs.holycross.edu/~nfernand/Posters/Jack.pdf

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

Research Associates: Jiaqi Fang, Haoming Wu

Topics Investigated:

The interplay between quandles and codes.
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: Jiaqi Fang, Haoming Wu

Topics Investigated in the Weiss Research Program:

Cycle types of reversed Dickson permutation polynomials.
Complete permutation polynomials arising from reversed Dickson polynomials.
Quandles, shelves, racks.
Partially ordered Sets.
Lotka-Volterra equations
Operations research.

Research Articles:

Jiaqi Fang, Neranga Fernando, Haoming Wu, Reversed Dickson polynomials , Involve, a Journal of Mathematics 18-2 (2025), 297 – 328

Dissemination of Results:

Jiaqi and Haoming presented their research results of the Weiss Program at

Weiss Summer Research Symposium at College of the Holy Cross, September 8, 2023,
AMS sectional meeting at the University of South Alabama, October 13 – 15, 2023, and
Academic Conference at College of the Holy Cross, April 24, 2024.

The posters of Jiaqi and Haoming presented at the Weiss Summer Research Symposium can be accessed through the following links:

https://mathcs.holycross.edu/~nfernand/Posters/Jiaqi.pdf
https://mathcs.holycross.edu/~nfernand/Posters/Ming.pdf

Northeastern University, Boston, MA

Noah Lichtblau
Research Topic: Fibonacci Numbers and Zumkeller Numbers.
Walker Miller-Breetz
Research Topic: Polynomial g_{n,q}.
Jackson Steilberg
Research Topic: Functional Graphs.
Yuval Timen
Research Topic: Permutation polynomials over finite fields arising from Lucas polynomials.
Aliya Tyshkanbayeva
Research Topic: Permutation polynomials over finite fields arising from Lucas polynomials.
Mohammad Rashid
Research Topic: Permutation polynomials over finite fields, self-reciprocal polynomials.
Research Article: N. Fernando, M. Rashid, Fibonacci self-reciprocal polynomials and Fibonacci permutation polynomials. arXiv:1712.07723.
Honors Project: Siddhartha Pant
Research Topic: Dickson polynomials over finite fields.
Luke Kyungmin Shin
Research Topic: Permutation polynomials over finite fields.

University of South Florida, Tampa, FL

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

Research Grants,Travel Grants and Stipends

Conference Travel Award from Eleanor Zweifel and Anne Zweifel Taylor Fund - Knox College 2025/2026.
Research grant from the J.D. Power Center at College of the Holy Cross - Spring 2025
Provost’s Supplemental Research Fund, College of the Holy Cross - Fall 2024
Research grant from the J.D. Power Center at College of the Holy Cross - Fall 2024
Stipend for mentoring three undergraduate students - Weiss Summer Science Research program at College of the Holy Cross - Summer 2024
Research grant from the J.D. Power Center at College of the Holy Cross - Fall 2023
Travel grant - College of the Holy Cross - Spring 2023
Stipend for mentoring two undergraduate students - Weiss Summer Science Research program at College of the Holy Cross - Summer 2023
Full-time Faculty Development Fund, Office of the Provost, Northeastern University - Spring 2016.

Professional Services

Prepared the Annual Stephens Scholarship Examination in Mathematics at Knox College which was held in December, 2025.
Served as the organizer of student research talks in the Department of Mathematics and Computer Science at College of the Holy Cross in the academic year 2024/2025.
Co-organizer of the research talks by math majors at the Academic Conference which will be held at College of the Holy Cross on April 23, 2025.
Served as the organizer of the faculty seminar in the Department of Mathematics and Computer Science at College of the Holy Cross in the academic year 2022/2023 (5 talks). https://mathcs.holycross.edu/~nfernand/seminar.html
Served as the organizer of the faculty seminar in the Department of Mathematics and Computer Science at College of the Holy Cross in the academic year 2023/2024 (8 talks). https://mathcs.holycross.edu/~nfernand/seminar.html
Served as the Calculus Coordinator in the Department of Mathematics and Computer Science at College of the Holy Cross in the academic year 2023/2024.
Served as the Library Liaison in the Department of Mathematics and Computer Science at College of the Holy Cross in Spring 2022.
Served as the coordinator for Calculus 2, and 3 for Science and Engineering at Northeastern University in Spring 2015 and Summer 1 2015, respectively.
Served on the space committee in the Department of Mathematics at Northeastern University in the Academic Year 2018 - 2019.

William Lowell Putnam Mathematical Competition

Prepared math majors at Knox College for the Putnam Competition which was held in December, 2025.
Co-organized help sessions at the College of the Holy Cross for the Putnam Competition which was held in December, 2024.

Journal Referee

Proceedings of the London Mathematical Society
Journal of Pure and Applied Algebra
Journal of Number Theory
Finite Fields and Their Applications
Discrete Mathematics
Journal of Algebra and its Applications
Journal of Algebra Combinatorics Discrete Structures and Applications
FILOMAT
Mathematica Slovaca
International Journal of Foundations of Computer Science
Applicable Algebra in Engineering, Communication, and Computing
Cryptography and Communications
Algebra Colloquium
Indagationes Mathematicae
Arabian Journal of Mathematics
Open Mathematics

Zentralblatt MATH -

I have been a reviewer for Zentralblatt MATH since 2017.

AMS Math Review -

I have been a reviewer for Mathematical Reviews since 2017.

Professional Memberships

American Mathematical Society
Canadian Mathematical Society
London Mathematical Society
New Zealand Mathematical Society

Awards, Academic Achievements and Scholarships

First class honours in B.Sc.(special degree) majoring Mathematics, University of Kelaniya, Sri Lanka, 2007
Recipient of the Gold medal in Mathematics at the University of Kelaniya, Sri Lanka, 2007
Graduate Teaching Assistantship in the Department of Mathematics and Statistics at the University of South Florida from Spring 2008 to Spring 2013
Tharp Scholarship, University of South Florida in 2010
Provost’s Certificate of Recognition for outstanding performance as a Graduate Teaching Assistant in University of South Florida in 2010
Tharp Scholarship, University of South Florida in 2011
Provost’s Certificate of Recognition for outstanding performance as a Graduate Teaching Assistant in University of South Florida in 2012
Tharp Scholarship, University of South Florida in 2012
Professor Appreciation Award, Black Engineering Student Society, Northeastern University, April 11th, 2014.
Eugene P. Shelly Visiting Assistant Professor Position at Carnegie Mellon University, a position created through a gift of Eugene P. Shelly, 2019.

Community Outreach

CIMPA School in Sri Lanka in 2028 - Currently collaborating with three colleagues based in France, USA and Sri Lanka to organize a CIMPA School at the University of Kelaniya to provide training in contemporary pure and applied mathematics for students, young researchers, and teacher-scholars in Sri Lanka.
Supporting/Mentoring students from underrepresented groups - At an AMS sectional meeting at the University of North Texas in September 2017, mentored African-American students from Mcdonogh 35 High School interested in mathematics, providing guidance on university admission, academic careers, and research opportunities; connected students with faculty at Northeastern University, leading to their presentation on Embeddings of H4 Polytopes in the Special Session on Polytopes and Discrete Geometry, VI at an AMS meeting held at Northeastern University in April, 2018.