My research is in Universal Algebra.
I am currently studying clonoids.
A clonoid from an algebra A to an algebra B is a set of functions from finite powers of A into B
that are closed first with respect to composition with term functions of A and next with respect to composition with term functions on B.
Clonoids have been used in studying equational theories of finite algebras, classifying expansions of algebras,
and investigating the computational complexity of Promise Constraint Satisfaction Problems.
In the below preprint, Clonoids between modules, we study clonoids whose source and target are abelian Mal'cev algebras (algebras that are polynomially equivalent to modules).
Current work connects clonoids to central extensions.
In particular, we can understand the structure of a 2-nilpotent Mal'cev algebra by understanding two abelian algebras and a clonoid from one to the other.
Publications and Preprints
P. Mayr and P. Wynne.
Clonoids between modules.
Submitted 2023.
[pdf]
Talks
The Subpower Membership Problem for Nilpotent Mal'cev Algebras (Invited Talk).
Association for Symbolic Logic North America Meeting, Iowa State University, May 2024.
The Finite Basis Problem for Nilpotent Mal'cev Algebras.
BLAST Conference 2024, University of North Texas, April 2024.
Clonoids and Nilpotent Algebras.
Panglobal Algebra and Logic Seminar, University of Colorado Boulder, October 2023. [slides] [video]
Clonoids Between Abelian Groups.
BLAST Conference 2023, University of North Carolina Charlotte, May 2023.
On the Number of Clonoids Between Finite Modules.
BLAST Conference 2022, Chapman University, August 2022.
Nilpotent Extensions of Mal’cev Algebras.
Equations in Universal Algebra Research Seminar, Johannes Kepler University, June 2022.
Clonoids Between Finite Modules.
Workshop on General Algebra, AAA 102 University of Szeged, Hungary, June 2022.
On Clonoids Between Abelian Groups of Coprime Order.
Workshop on General Algebra, AAA 101, University of Novi Sad, Serbia, June 2021.
Some Finiteness Results in Universal Algebraic Geometry.
Ulam Seminar, University Of Colorado Boulder, April 2021.
Post's Correspondence Problem.
Graduate Student Seminar, University of Colorado Boulder, November 2020.
