Alexis Hardesty, PhD

Assistant professor, TWU Division of Mathematics

Contact

Office: MCL 416
Email: ahardesty1@twu.edu

Research interests

• The application of homological methods to commutative algebra.
• Differential graded algebra structures on free resolutions.

Teaching

Courses I have taught at TWU:

• College Algebra (Math 1303)
• Discrete Mathematics (Math 3013)
• Abstract Algebra (Math 3053)
• Number Theory (Math 3083/5523)
• Calculus 1 (Math 2014)
• Linear Algebra (Math 3063) 

Curriculum development

Courses I have worked on with curriculum development teams:

• Calculus I, II and III at Texas Tech University (2022-23)
• Introduction to Proofs at Texas Tech University (2018-19)

Publications/preprints

Realizing Algebra Structures on Free Resolutions of Grade 3 Perfect Ideals, submitted.

Sampling algebra structures on minimal free resolutions of length 3. (with L. Christensen and O. Gotchey), in Experimental Mathematics.

The Eliahou-Kervaire resolution over a skew polynomial ring. (with L. Ferraro), in Communications in Algebra

The Tor Algebra of Trimmings of Gorenstein Ideals. (with L. Ferraro), in Acta Mathematica Vietnamica

Apéry-like numbers and families of newforms with complex multiplication.= (with D. McCarthy and S. Young), in Research in Number Theory

Invited talks at conferences

Joint Mathematics Meetings 2025: "A Macaulay2 Algorithm to Realize Tor Algebra Structures of Grade 3 Ideals" 

Joint Mathematics Meetings 2023: "The Eliahou-Kervaire resolution over a skew polynomial ring"

MAA MathFest 2024: "Realizing Groups of Order 2^n via Groups of Units"

MAA MathFest 2023: "Classifying Ideals Based on Multiplicative Structures in Homology"

Southwest Local Algebra Meeting 2023: "Realizing Differential Graded Algebra Structures on Minimal Free Resolutions"

Southwest Local Algebra Meeting 2022: "A DG Algebra Resolution of Trimmings of Pfaffian Ideals"

SLMath Connections Workshop 2023: "Sampling Algebra Structures on Minimal Free Resolutions of Length 3"

Conference on Homological Commutative Algebra and Related Topics 2022: "Differential Graded Algebra Structures on Minimal Resolutions of Local Rings"

Activities

Outside of research and teaching, I participate in various professional development activities, detailed below.

Professional development

MAA Project NExT (2023-2024)

Women in Commutative Algebra (WiCA) Research Network (2023-present)