LogoResources – Universal Algebra – Institute for Algebra – JKU

Here you can find some presentations by members of the Institute for Algebra at JKU Linz in the field of Universal algebra.

Conference and Colloquium Talks

2019 Solving Systems of Equations in Supernilpotent Algebras
Erhard Aichinger at MFCS 44, Aachen, Germany, August 2019
2019 Clones of Polynomials
Erhard Aichinger at AAA98, Dresden, Germany, June 2019
2019 Solving equations in finite algebras
Erhard Aichinger at University Vienna, Austria, May 2019
2019 Polynomial maps on supernilpotent algebras
Erhard Aichinger at AAA97, Vienna, Austria, March 2019
2018 Polynomial Completeness in Expanded Groups -- Talk in Honour of Kalle Kaarli's Birthday
Erhard Aichinger at Algebra and its Applications, Tartu, Estonia, July 2018
2018 Bounding the free spectrum of nilpotent algebras of prime power order
Erhard Aichinger at AAA96, Darmstadt, Germany, June 2018
2018 Clonoids
Erhard Aichinger at AAA95, Bratislava, Slovakia, February 2018
2017 Mal'cev clones on finite sets
Erhard Aichinger at NSAC2017+AAA94, Novi Sad, Serbia, June 2017
2017 Lattices allowing only nilpotent commutator operations
Erhard Aichinger at AAA93, Bern, Switzerland, February 2017
2015 Forks, finitely related clones, and finitely generated varieties
Erhard Aichinger at SSAOS 53, Srní, Czech Republic, 2015 (with exercises)
2015 Independence of algebras
Erhard Aichinger at AAA90, Novi Sad, Serbia, June 2015
2014 Term functions of direct products
Erhard Aichinger at AAA88, Warsaw, Poland, June 2014
2014 Subvarieties and Clones
Erhard Aichinger at AAA87, Linz, Austria, February 2014
2013 Higher commutators, nilpotence, and supernilpotence
Erhard Aichinger at NSAC 2013, Novi Sad, Serbia, 2013
2013 Algebraische Zugänge zur Beschreibung von Mal'cev-Klonen
Erhard Aichinger at TU Dresden, Germany, January 2013
2012 Polynomial completeness properties
Erhard Aichinger at AAA84, Dresden, Germany June 2012
2012 Polynomials and Structure of Universal Algebras
Erhard Aichinger at TU Wien, January 2012
2011 A remark on the composition of polynomial functions over algebraically closed fields
Erhard Aichinger at AAA81, Salzburg, Austria, February 2011
2010 Polynomial Completeness of Mal'cev Algebras
Erhard Aichinger at AAA79, Olomouc, Czech Republic, February 2010
2009 An instance of the subnear-ring membership problem
Erhard Aichinger at Near-rings and Near-fields Vorau, Austria, July 2009
2008 The surprising ubiquity of planar near-rings
Erhard Aichinger at Combinatorics 2008, Costermano, Italy, July 2008 (helpful comments by Peter Mayr are gratefully acknowledged)
2007 Informationstheorie – eine mathematische Theorie der Datenkompression und Datenübertragung
Erhard Aichinger at Tag der Mathematik für Mathematiklehrerinnen und -lehrer an der JKU Linz, November 2007
2007 Some applications of higher commutators to Mal'cev algebras
Erhard Aichinger at AAA75, Darmstadt, Germany, November 2007 (joint research with Nebojsa Mudrinski)
2007 Congruence preserving functions and polynomial functions on expanded groups
Erhard Aichinger at Near-rings 2007, Linz, Austria, July 2007
2007 On the number of polynomially inequivalent Mal'cev algebras with congruence lattice of height two
Erhard Aichinger at AAA73, Klagenfurt, Austria, February 2007 (joint research with Nebojsa Mudrinski)

Local talks

Talks given at seminars at JKU Linz:
2019 The Complexity of Solving Equations over Finite Groups – A collection of results by Goldmann and Russell from 1999
Philipp Nuspl in the Literature seminar Universal Algebra und Computational Complexity, March 2019

Lecture Notes

For some of our lectures, we have provided lecture notes.
2010 Lineare Algebra und Analytische Geometrie
2009 Kommutative Algebra und algebraische Geometrie
2012 Einf├╝hrung in die Algebra und Diskrete Mathematik
2007 Informations- und Codierungstheorie (Informationstheorie)
2019 Überblick Mathematik für NawiTec. Teil I (Lineare Algebra und Vektorrechnung), Teil II (Wahrscheinlichkeitstheorie), Teil III (Differential- und Integralrechnung)

Software

2015 GAP package SONATA: Systems of nearrings and their applications Erhard Aichinger, Franz Binder, Jürgen Fuß, Peter Mayr, Christof Nöbauer.
2018 GAP package Predicata: Deciding Presburger Arithmetic Using Automata Theory Fritz Kliemann
2019 Using group theory for solving Rubik's cube in GAP Paul Kainberger
Maintained by Erhard Aichinger and Philipp Nuspl.