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Amanda Welch
Introduction Education & Training Research & Creative Interests Publications Frequently Taught Courses Funding & Grants Professional Affiliations Update your profile

Amanda Welch

Assistant Professor of Mathematics Office: 3212 - Old Main
Email: arwelch@eiu.edu

INTRODUCTION

Amanda Welch (she/her/hers) received her PhD in Mathematics from Virginia Tech University in 2019. Her dissertation work was in the field of Algebraic Combinatorics. After Virginia Tech, Amanda was a Visiting Professor at the College of the Holy Cross from Fall 2019 through Spring 2021. In Fall 2021, she began at Eastern Illinois University, where she holds the position of Assistant Professor of Mathematics.

Education & Training

  • Virginia Tech University, Blacksburg, VA
    • Doctor of Philosophy in Mathematics, Spring 2019 
      • Advisor: Daniel Orr
      • Dissertation: Double Affine Bruhat Order
      • Area of Mathematics: Algebraic Combinatorics
    • Master of Science in Mathematics, Spring 2015
      • Advisor: Peter Linnell
      • Thesis: Characterizing Zero Divisors of Group Rings
      • Area of Mathematics: Algebra
  • Northern Kentucky University, Highland Heights, KY           
    • Bachelor of Science in Mathematics, Spring 2013
      • Advisor: Aimee Krug  
      • Senior Capstone: Combinatorial Game Theory and the Game of Greedy Cannibals
      • Area of Mathematics: Combinatorial Game Theory

Research & Creative Interests

My research interests lie in the fields of Algebra, Combinatorics, Number Theory, and their intersections. Specifically, I study Integer Partitions, which count the number of ways to sum to a fixed non-negative integer n using positive integers, and Dynamical Algebraic Combinatorics, which studies the interaction of mathematical objects and actions to examine such things as homomesy, row motion, and the cyclic sieving phenomenon. A list of selected works is given below and pre-prints for my publications can be found on the math ArXiv.

 

Both areas of research have potential for student projects. Any interested students should email me at the address listed above for more information.

Publications

 

  1. Cyclic Sieving on Permutations - An Analysis of Maps and Statistics in the FindStat Database, with Ashleigh Adams, Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Submitted February 2024

  2. Generalizations of PED and POD Partitions, with Cristina Ballantine, Submitted August 2023 

  3. Toggling, Rowmotion, and Homomesy on interval-closed sets, with Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Accepted August 2023 to the Journal of Combinatorics 

  4. Homomesies on Permutations – An Analysis of Maps and Statistics in the FindStat Database, with Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Accepted to Mathematics of Computation, May 2023

  5. Beck-type companion identities for Franklin’s identity, with Cristina Ballantine, Contributions to Discrete Mathematics, 18(1), (2023) 

  6. PED and POD Partitions: Combinatorial Proofs of Recurrence Relations, with Cristina Ballantine, Discrete Mathematics, 346 (3) (2023) 113259. https://doi.org/10.1016/j.disc.2022.113259.
  7. Classification of Cocovers in the Double Affine Bruhat Order, The Electronic Journal of Combinatorics, 29(4), (2022), https://doi.org/10.37236/10745
  8. Beck Type Identities For Euler Pairs Of Order r, with Cristina Ballantine, In: Bostan A., Raschel K. (eds) Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019. Springer Proceedings in Mathematics & Statistics, vol 373. Springer, Cham. (2021) https://doi.org/10.1007/978-3-030-84304-5_6
  9. Beck-Type Companion Identities for Franklin’s Identity via a Modular Refinement, with Cristina Ballantine, Discrete Mathematics, 344 (8) (2021) 112480, 11 pp.
  10. Beck-Type Identities: New Combinatorial Proofs and a Modular Refinement, with Cristina Ballantine, Ramanujan J 58, 943-955 (2022). https://doi.org/10.1007/s11139-021-00469-w

Frequently Taught Courses

  • CSM 3770: Combinatorial Computing
  • MAT 1170: Problem Solving
  • MAT 1160: Mathematics: A Human Endeavor
  • MAT 2880: Foundations of Mathematics
  • MAT 2550: Introduction to Linear Algebra
  • MAT 1441: Calculus 1
  • MAT 2442: Calculus 2

Funding & Grants

  • EIU DFW Collaborative Redesign Initiative Grant for MAT 1160: Mathematics: A Human Endeavor
  • EIU FDIC Professional Development Grant, Fall 2023
  • EIU Summer Research/Creative Activity Award, Summer 2023
  • EIU Redden Grant for Support in Purchasing Online Material for Calc 2, Summer 2023
  • AWM Mathematical Endeavors Revitalization Program (MERP) award, March 29, 2023
  • Collaborate@ICERM workshop funding for travel and board, January 9 – 13, 2023
  • ICERM fellowship for participating in "Research Community in Algebraic Combinatorics" program Aug 2021 – Feb 2022

Professional Affiliations

  • Association for Women in Mathematics (AWM)
  • Illinois Council for Teachers of Mathematics (ICTM)
  • Kappa Mu Epsilon Math Honors Society (KME)
  • American Mathematical Society (AMS)