About Me

My name is Anna Natalie Chlopecki (she/her), and I am a mathematics graduate student at Purdue University. I grew up in the Chicago Metropolitan Area of Illinois. In 2020, I graduated from the University of Illinois at Urbana-Champaign with a BS in Mathematics and a minor in Criminology, Law, and Society. My research interests are rooted in combinatorial commutative algebra and computational algebraic geometry. I am advised by Uli Walther and Eric Samperton. In my free time, I enjoy playing tennis and reading. I will be on the job market starting in the fall of 2026.

Contact Information

Email: achlopec@purdue.edu
Address: Mathematical Sciences Building, 150 N. University Street, Office 1047, West Lafayette, IN

Curriculum Vitae

Combinatorial Commutative Algebra

I am investigating determinantal ideals of matrices of linear forms. Currently, I am studying a special case stemming from graphs, hoping to identify a criterion as to when the associated ideal is Hilbertian, i.e. its Hilbert function and polynomial agree for all non-negative integer inputs.

Computational Algebraic Geometry

I am interested in the computational complexity of counting problems rooted in algebra and geometry. At present, I would like to better understand "how hard" it is to count the number of homomorphisms between two groups.

Mentorship

During the spring of 2025, I was the graduate student mentor for an undergraduate research project through the Purdue Experimental Mathematics Lab. Under the guidance of Eric Samperton and myself, undergraduates Shannon Cheng and Saarah Nazar developed an interactive applet to illustrate a reduction from the Independent Set Problem to the Trivial Sublink Problem.

Preprints

(3) Antidiagonal Initial Complexes of Infinite Matrix Schubert Varieties are Cohen-Macaulay. With Nathaniel Gallup and Jason Meintjes. Submitted 2026.
(2) An elementary proof that linking problems are hard. With Shannon Cheng, Saarah Nazar, and Eric Samperton. Submitted 2025.
(1) Permutation polynomials: iteration of shift and inversion maps over finite fields. With Juliano Levier-Gomes, Wayne Peng, Alex Shearer, and Adam Towsley. 2021.

Current students can find course notes using the links below.

Instructor of Record

Linear Algebra (MA 26500), Spring 2026
Applied Calculus I (MA 16010), Fall 2024 and Spring 2026

Recitation Instructor

Multivariate Calculus (MA 26100), Fall 2022 and Summer 2024
Analytic Geometry and Calculus I (MA 16500), Fall 2020

Grader

Elements of Algebra I (MA 45300), Spring 2023, 2024, and 2025
Linear Algebra II (MA 35301), Fall 2023
An Intro to Proof through Real Analysis (MA 30100), Fall 2023
Diff. Eq. and Partial Diff. Eq. for Engineering and the Sciences (MA 30300), Summer 2022

Below are the initiatives I am currently a part of. For prior involvement, please consult my CV.

Bridge to Research

Organizer (with Jelena Mojsilovic and Benjamin Mudrak)
Graduate student seminar which offers Purdue Math Department faculty the space to provide an introduction into their research area. Especially useful for those in search of a research advisor or direction.

Association for Women in Mathematics

Vice President
Focused on supporting women in the Purdue Math Department via social and professional development events. Notable efforts include the Math Mentor Program for first-year graduate students and the Purdue Annual AWM Symposium, a "mini conference" for gender minorities to showcase their research. For further information, please visit our webpage.

ANNA NATALIE CHLOPECKI