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Map of Science

Mayr, Peter

Associate Professor

Positions

• Associate Professor, Mathematics

Research Areas

• Algebra
• Mathematical Foundations

Research

research overview

• My main research area is Universal Algebra with connections to Logic and Computer Science. General algebraic structures come up for example in connection with Constraint Satisfaction Problems (CSP) which generalize Boolean satisfiability, graph coloring, and scheduling problems. A typical question is then how to classify and represent these structures and how to compute with them efficiently.

keywords

• universal algebra, computational complexity

Publications

selected publications

• conference proceeding

  • On the Complexity Dichotomy for the Satisfiability of Systems of Term Equations over Finite Algebras.  Leibniz International Proceedings in Informatics. 66:1-66:12. 2023
  • Quantified Constraint Satisfaction on Monoids.  15:1-15;14. 2016
  • Difference methods and Ferrero pairs.  177-187. 2003
  • Algorithms for finite near-rings and their N-groups.  Journal of Symbolic Computation. 23-38. 2000
  • Algorithms for near-rings of non-linear transformations.  23-29. 2000

• journal article

  • Clonoids between modules.  International Journal of Algebra and Computation. 543-570. 2024
  • Vaughan-Lee's nilpotent loop of size 12 is finitely based.  Algebra Universalis. 2024
  • SMALL PROMISE CSPS THAT REDUCE TO LARGE CSPS.  Logical Methods in Computer Science. 2022
    
  • Algebras from congruences.  Algebra Universalis. 2021
  • Sandwiches for promise constraint satisfaction.  Algebra Universalis. 2021
  Bounded homomorphisms and finitely generated fiber products of lattices.  International Journal of Algebra and Computation. 693-710. 2020
  
  PRESENTATIONS FOR SUBRINGS AND SUBALGEBRAS OF FINITE CO-RANK.  Quarterly Journal of Mathematics. 53-71. 2020
  Generating subdirect products.  Journal of London Mathematical Society. 404-424. 2019
  
  THE SUBPOWER MEMBERSHIP PROBLEM FOR FINITE ALGEBRAS WITH CUBE TERMS.  Logical Methods in Computer Science. 2019
  
  Solvable quotients of subdirect products of perfect groups are nilpotent.  Bulletin of the London Mathematical Society. 1016-1026. 2018
  
  Finiteness properties of direct products of algebraic structures.  Journal of Algebra. 167-187. 2018
  The subpower membership problem for semigroups.  International Journal of Algebra and Computation. 1435-1451. 2016
  Finitely generated equational classes.  Journal of Pure and Applied Algebra. 2816-2827. 2016
  Independence of algebras with edge term.  International Journal of Algebra and Computation. 1145-1157. 2015
  SUPERNILPOTENCE PREVENTS DUALIZABILITY.  Journal of the Australian Mathematical Society. 1-24. 2014
  On the number of finite algebraic structures.  Journal of the European Mathematical Society. 1673-1686. 2014
  On finitely related semigroups.  Semigroup Forum. 613-633. 2013
  THE SUBPOWER MEMBERSHIP PROBLEM FOR MAL'CEV ALGEBRAS.  International Journal of Algebra and Computation. 2012
  CHARACTERIZING TRANSLATIONS ON GROUPS BY COSETS OF THEIR SUBGROUPS.  Communications in Algebra. 3141-3168. 2012
  Units of compatible nearrings.  Monatshefte fuer Mathematik. 119-132. 2011
  Mal'cev algebras with supernilpotent centralizers.  Algebra Universalis. 193-211. 2011
  Polynomial functions on subdirect products.  Monatshefte fuer Mathematik. 341-359. 2010
  Frobenius complements of exponent dividing 2(m) . 9.  Forum Mathematicum. 217-220. 2009
  Polynomial clones on squarefree groups.  International Journal of Algebra and Computation. 759-777. 2008
  A topological property of polynomial functions on $${rm{GL}(2, mathbb {R})}$$.  Aequationes Mathematicae. 71-77. 2007
  Polynomial clones on groups of order pq.  Acta Mathematica Hungarica. 267-285. 2007
  Sharply 2-transitive groups with point stabilizer of exponent 3 or 6.  Proceedings of the American Mathematical Society. 9-13. 2006
  The polynomial functions on Frobenius complements.  Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 37-50. 2006
  The polynomial functions on Frobenius complements.  Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 37-50. 2006
  Fixed-point-free automorphism groups from rings.  Southeast Asian Bulletin of Mathematics. 253-257. 2005
  Polynomial functions and endomorphism near-rings on certain linear groups.  Communications in Algebra. 5627-5651. 2003
  Nearrings whose set of N-subgroups is linearly ordered.  Results in Mathematics. 339-348. 2002
  Algorithms for finite near-rings and their N -groups.  Journal of Symbolic Computation. 23-38. 2001
  ... more

Teaching

courses taught

• MATH 2001 - Introduction to Discrete Mathematics
  Primary Instructor - Spring 2018 / Spring 2020 / Fall 2020
  Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
• MATH 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
  Primary Instructor - Fall 2021
  Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
• MATH 2135 - Introduction to Linear Algebra for Mathematics Majors
  Primary Instructor - Fall 2018 / Spring 2019 / Fall 2019 / Fall 2024
  Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
• MATH 3140 - Abstract Algebra 1
  Primary Instructor - Fall 2021 / Spring 2024
  Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
• MATH 4000 - Foundations of Mathematics
  Primary Instructor - Fall 2024
  Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Same as MATH 5000.
MATH 4140 - Abstract Algebra 2
Primary Instructor - Spring 2024
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140.
MATH 5000 - Foundations of Mathematics
Primary Instructor - Fall 2024
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Department enforced prerequisites: MATH 2130 and MATH 3140. Same as MATH 4000.
MATH 5140 - Abstract Algebra 2
Primary Instructor - Spring 2024
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Department enforced prerequisite: MATH 3140. Same as MATH 4140.
MATH 6010 - Computability Theory
Primary Instructor - Spring 2019 / Spring 2021 / Fall 2023
Studies the computable and uncomputable. Shows that there are undecidable problems and from there builds up the theory of sets of natural numbers under Turing reducibility. Studies Turing reducibility, the arithmetical hierarchy, oracle constructions and end with the finite injury priority method. Department enforced prerequisite: MATH 6000.
MATH 6140 - Algebra 2
Primary Instructor - Spring 2018 / Spring 2022
Studies modules, fields and Galois theory. Department enforced prerequisite: MATH 6130. Instructor consent required for undergraduates.
MATH 6270 - Theory of Groups
Primary Instructor - Fall 2019
Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.
... more

Background

education and training

• Dr. habil., Johannes Kepler University Linz (Austria) 2013
• Ph.D., Johannes Kepler University Linz (Austria) 2004
• M.S., Johannes Kepler University Linz (Austria) 1999

International Activities

geographic focus

• Austria  Country
• Canada  Country
• Czech Republic  Country
• Europe  Continent
• Russian Federation  Country
Spain  Country
United Kingdom  Country
... more

Other Profiles

ORCID iD

• http://orcid.org/0000-0003-1163-313X

Google Scholar

• https://scholar.google.co.uk/citations?hl=en&user=kzH2RCUAAAAJ&scilu=863266149077478822:0,1502397146782920377:0,6824191684339624486:0,8139594160244975023:0,8166924715003519978:0,9532761288362058660:0,10787747879176351656:0,11867367175766399844:0,130904597

ResearchGate

• https://www.researchgate.net/profile/Peter_Mayr

Github

• https://github.com/PMayr