Li-An Chen - Mathematics

Research interests

I'm working on polynomials over finite fields, and relevant topics motivated by their application to cryptography. I'm also interested in applying combinatorial optimization methods to these problems.

In general, I like several areas in discrete mathematics. Previously, I've worked on an algebraic approach on a variety of Erdős-Ko-Rado theorem (summer project) and analytic combinatorics (Master's thesis--see the link below). I occasionally dabble in number theory.

Before joining math graduate schools, I was interested in hydraulics and river morphology and involved in some undergraduate computational research that used Matlab and Fortran. (I still love rivers and ocean in a non-academic way!)

Papers

On the preimage distribution of $x^2+L(x)$, with Robert S. Coulter, 14 pages manuscript, in preparation.
Algorithms for computing the permutation resemblance of functions over finite groups, with Robert S. Coulter, Mathematics of Computation, 94 (2025), 1543-1570.
Permutation resemblance, with Robert S. Coulter, IEEE Transactions on Information Theory, 69 (2023), no. 10, 6711-6718.
Bounds on the differential uniformity of the Wan-Lidl permutation polynomials, with Robert S. Coulter, Cryptography and Communications, 15 (2023), 1069-1085.

Peer-reviewed conference abstracts

On the differential uniformity of the Wan-Lidl permutation polynomials, 4 page extended abstract, The 7th International Workshop on Boolean Functions and their Applications (BFA), 2022.

Theses

Resemblance of polynomials over finite fields and related topics, Ph.D. Thesis, University of Delaware, 2023. (Abstract and contents)
Probabilistic analysis of the total cophenetic index in phylogenetic trees, Master's Thesis, National Chiao Tung University, 2015.
One of the two awardees of TMS Outstanding Master's Thesis Prize in 2015 selected by Taiwanese Mathematical Society (aka The Mathematical Society of the Republic of China).

Academic Visits

Probabilidad y Estadística, Centro de Investigación en Matemáticas (CIMAT), Guanajuato, Gto, Mexico. (June 1 to July 30, 2025)
Hosts: James Melbourne and Emma Pollard.
Department of Mathematical Sciences, The University of Memphis, Memphis, TN, USA. (March 18 to 23, 2025)
Host: Dheer Noal.
Travel supported by the Department of Mathematical Sciences, The University of Memphis.

Recent talks, posters, and workshop participation (2024~)

15-minute talk (Short Communication): "Permutation resemblance" (July 2026)
International Congress of Mathematicians (ICM), Section 14 - Mathematics of Computer Science, Pennsylvania Convention Center, Philadelphia, PA, USA.
Travel supported by AMS - ICM 2026 Early-Career Mathematician Travel Grant award (NSF Grant No. 2620718) and the Department of Mathematics, Boise State University.
Workshop attendee: (May 2026)
11th Lake Michigan Workshop on Combinatorics and Graph Theory, The University of Notre Dame, Notre Dame, IN, USA.
Travel supported by the Department of Mathematics, Boise State University.
Invited 60-minute keynote talk: "Permutation Resemblance" (August 2025)
The 32nd New-sprout Symposium for Young Combinatorists (第32屆組合數學新苗研討會), Fu Jen Catholic University (輔仁大學), New Taipei City, Taiwan.
20-minute talk: "Computation and application of permutation resemblance" (July 2025)
International Conference on Finite Fields and Their Applications 2025 (Fq16), Universidade de São Paulo, São Carlos, SP, Brazil.
Travel supported by the Department of Mathematics, Boise State University.
50-minute talk: "Permutation Resemblance" (March 2025)
Colloquium, Department of Mathematical Sciences, The University of Memphis, Memphis, TN, USA.
Travel supported by the Department of Mathematical Sciences, The University of Memphis.
Workshop attendee: "Lattices and their Applications in Communications" (July 2024)
Diversity in Finite Fields and Coding Theory, Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, RJ, Brasil.
Project leaders: Cintya W. O. Benedito and Grasiele C. Jorge.
Travel supported by IMPA and Boise State University (Department of Mathematics, and College of Arts and Sciences - Faculty Travel Grant).
50-minute talk: "Permutation resemblance: an integer programming approach" (March 2024)
Analysis and Dynamics Seminar, Department of Mathematics, University of Denver, Denver, CO, USA.

Archived talks, posters, and workshop participation (~2023)

50-minute talk: "Permutation Resemblance" (September 2023)
Topics in Algebra, Topology, Etc., Research Seminar (TATERS), Department of Mathematics, Boise State University, Boise, ID, USA.
20-minute talk: "On the preimage distribution of $x^2+L(x)$ over $\ff{p^2}$" (June 2023)
International Conference on Finite Fields and Their Applications 2023 (Fq15), Paris, France.
20-minute talk: On the differential uniformity of the Wan-Lidl permutation polynomials (September 2022)
The 7th International Workshop on Boolean Functions and their Applications (BFA 2022), Balestrand, Norway.
Travel supported by the University of Delaware (Department of Mathematical Sciences and Graduate College).
10-minute talk: "Algorithms for computing the permutation resemblance of functions on finite groups" (April 2022)
Joint Mathematics Meetings (JMM2022): AMS Contributed Paper Session on Codes, Partitions, and Permutations. Online.
50-minute talk: "Permutations over Finite Fields with Low Differential Uniformity" (2022)
Hallenbeck Graduate Student Seminar (HGSS), Department of Mathematical Sciences, University of Delaware.
Poster: "Polynomials over Finite Fields with Low Differential Uniformity" (February 2022)
Winter Research Symposium, Department of Mathematical Sciences, University of Delaware.
50-minute talk: "Algorithms for computing the permutation resemblance of functions on finite groups" (November 2021)
Discrete Mathematics/Algebra Seminar, University of Delaware.
50-minute talk: Exponential Sums for Finite Fields and Their Application (March 2021)
Hallenbeck Graduate Student Seminar (HGSS), University of Delaware.
20-minute talk: "Application of Linear Programming for Computing the Permutation Resemblance of Polynomials Over Finite Fields" (February 2021)
Winter Research Symposium, Department of Mathematical Sciences, University of Delaware.
Poster: The Number of Distinct Values of Almost Perfect Nonlinear Functions (February 2020)
Winter Research Symposium, Department of Mathematical Sciences, University of Delaware.

Other write-ups

Term Paper on the article of Natalia Tokareva titled "Algebraic normal form of a bent function: properties and restrictions", with Dheer Noal, Kamal Joshi, and Teddy Mishura (2019).
Final assessment for the course Topics in Mathematics: Boolean Functions and Application at the University of Delaware taught by Prof. Robert Coulter.
A Summary of Expected Distance Between Terminal Nucleotides of RNA Secondary Structures (2015).
Final assessment for the course Analytic Combinatorics at National Chiao Tung University taught by Prof. Micheal Fuchs.
Graph Theory Meets Biology : Phylogenetics (presentation slides) (2014).
Final assessment for the course Topics of Discrete Mathematics (II) at National Chiao Tung University taught by Prof. Ming-Hsuan Kang.

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