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  • Prüfungstermin
    Am 15.01.2016 von 08:30 bis 11:45 Uhr ist Prüfungstermin für "Algebra für InformatikerInnen" (SS15), "Einführung in die Algebra" (SS15) und "Kommutative Algebra" (SS15). Prüfungsanmeldung über Kusss erforderlich!


Science Park II, 3rd floor

Science Park II, 3rd floor, GPS: 48.335634,14.323747 ...  more of Location (Titel)

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Past Events

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Habilitationskolloquium Dr. Peter Mayr (Institut für Algebra)

Dienstag, 22. Oktober 2013, 14:00 Uhr

Room Change, now at UC 6, Uni-Center, JKU

Thema: "Finitely Related Algebras"

Abstract: In 1941 Emil Post showed that there are only countably many essentially distinct algebraic structures with two elements. Here algebras are considered as essentially equal (term equivalent) if they have the same term operations. For example, a Boolean lattice and the corresponding Boolean ring are term equivalent and will not be distinguished. On a finite set of size at least 3 the number of term inequivalent algebras is already continuum (Yanov, Muchnik, 1959). We show that only countably many of those have a group operation (Aichinger, Mayr, McKenzie, 2009). Moreover they are all implicitly determined by finitely many relations (that is, finitely related). This uses the classical Galois correspondence between term operations and invariant relations from Universal Algebra. We present some applications and connections of our results to rings, semigroups, and computations in direct powers of algebras, in particular, Constraint Satisfaction Problems (CSP).

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Startveranstaltung Mentoring Technische Mathematik

10. Oktober 2013, 15:30 - 17:00 Uhr, S2 048

Für den 10. Oktober 2013, 15:30-17:00 Uhr, S2 048 ist eine Informationsveranstaltung für StudienanfängerInnen der Studienrichtung Technische Mathematik geplant.

Unter dem Titel "Willkommen an der JKU - Informationen für Studierende der Technischen Mathematik" werden Peter Paule, RISC, Walter Zulehner, Vorsitzender der Studienkommission Technische Mathematik und Erhard Aichinger, Institut für Algebra in kurzen Vorträgen wichtige Informationen für StudienanfängerInnen bereitstellen. Die Vertreter der StV Mathematik werden ebenfalls anwesend sein.

ÖH StV Mathematik  (Neues Fenster)

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Thursday, 22. 8. 2013, 13:00 - 14:00, S3 057

Hubie Chen
(University of the Basque Country and Ikerbasque)

Generating Powers of Algebras: How, When, and Why

The quantified constraint satisfaction problem (QCSP) is the computational problem of deciding, given a structure and a first-order prenex sentence whose quantifier-free part is the conjunction of atoms, whether or not the sentence holds on the structure. One obtains a family of problems by defining, for each structure B, the problem QCSP(B) to be the QCSP where the structure is fixed to be B. We will discuss the research program of trying to classify the complexity of QCSP(B) for each finite structure B. It is possible to associate an algebra to each finite structure in such a way that studying the algebra of a structure gives insight into the QCSP complexity of the structure. We will overview the use of universal-algebraic notions and techniques in this research program. In particular, there is a close connection between QCSP complexity and the growth rate of the number of elements needed to generate the powers A^1, A^2, ... of an algebra A: showing an at-most polynomial growth rate can (essentially) be translated to a complexity upper bound for a structure with algebra A. This research area gives (we believe) a fascinating interplay between computational complexity, universal algebra, and logic.

This talk will partially be based on the overview article available at

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Abtrittsvorlesung Prof. Günter Pilz

"Unglaubliche Ergebnisse der Mathematik"

Mittwoch, 26.6.2013, 17:15, Hörsaal 19 (Science Park III)
(im Rahmen des „Kepler-Symposium“)


Viele Ergebnisse der Mathematik sind in dem Sinn langweilig, dass jeder diese Ergebnisse erwarten wird. Manchmal gibt es jedoch Resultate, die unserer Erwartung und Anschauung total widersprechen. Einige davon werden vorgestellt, wie etwa:

  • Warum konnte man in einer Biologie-Forschungsarbeit ohne Kenntnis der Materie erkennen, dass die Daten gefälscht waren?
  • Warum kann man manchmal durch die Sperre einer Durchzugstraße die Stauzeiten reduzieren?
  • Warum haben Männer oft die besseren Argumente, aber Frauen am Ende doch Recht?
  • Wie kann man sich mit einer langen Leiter in einem extrem engen Raum umdrehen?
  • Wieso wird ab Dimension 9 alles anders?

Mittelschulkenntnisse in Mathematik reichen vollkommen zum Verständnis.

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Linz Algebra Research Day, LARD 2013

JKU Linz, Wednesday, June 19, 2013

As in previous years the idea is that people from the different departments (RICAM, RISC, Algebra department, ...) doing research in algebra come together and give a brief, informal overview of their current work -- just so that people know what the others are doing.

Everybody is most cordially invited to give a talk. If you plan to do so, please send a title by June 14 to peter.mayr(/\t)
Presentations should be no longer than 10 minutes (on blackboard, no projector) and aiming at a general algebraic audience.

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WOLFRAM BENTZ (Centro de Álgebra da Universidade de Lisboa)
Dualizability and the ghost element method

Thursday, 13.06.2013, 13:45
Location: S2 053

Natural dualities, such as Stone duality, are useful because they
allow one to translate algebraic questions into the potentially
simpler and usually more intuitive setting of a topological structure.
Dualities are also tricky, in the sense that it takes a fair amount of
initial work to grasp the concept of a duality in its full generality.

Fortunately, there exist various established methods that allow one to
obtain results without having to review the complete underlying
theory. In this talk I will give a background on the ghost element
method, which is used to show the non-dualizibility of an algebra. It
was introduced by David and Werner to obtain the first such result.
More recently, P. Mayr and the author used it to show that any
super-nilpotent non-abelian algebra cannot be dualized. The talk will
include some demonstrations about how to obtain practical proofs using
this approach.

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Talk (Im Rahmen des Kepler-Symposiums):

WOLFRAM BENTZ (Centro de Álgebra da Universidade de Lisboa)
Quadratpackungen als mathematische Herausforderung

Wednesday, 12.06.2013, 17:15
Location: HS 13

Angenommen wir haben eine vorgegebene Anzahl gleichartiger Behälter
mit quadratischer Grundfläche, zum Beispiel Safttüten. Diese sollen
aufrecht in Containern transportiert werden, die ebenfalls eine
quadratische Basis haben. Um Platz zu sparen will man die Container so
klein wie möglich wählen. Wie groß sind die kleinstmöglichen
Container, und wie muss man die Behälter in einem solchen optimalen
Container platzieren? Fragen wie diese bezeichnet man als

Mathematisch bezeichnet geht es bei dem obigen Beispiel um
Quadratpackungen, deren Studium auf eine Arbeit von Erdös und Graham
zurückgeht. Für kleine Mengen zu packender Behälter wurden gute, und
vermutlich optimale Packungen auf verschiedene Weise gefunden.
Tatsächlich als optimal bewiesen wurde aber bisher nur eine zwar
unendliche, aber trotzdem überraschend beschränkte Anzahl von Fällen,
die zudem allesamt auf sehr simplen Packungen beruhen.

In diesem Vortrag, der auch für Studenten unterer Semester zugänglich
ist, geben wir eine Übersicht dieses Themas und legen die Methoden der
Optimalitätsbeweise dar.

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86th Workshop on General Algebra
86. Arbeitstagung Allgemeine Algebra (AAA86)

Olomouc, May 31 - June 2, 2013

application/pdfFirst Announcement (35KB, pdf)
AAA86 - further information  (Neues Fenster) Main Page of the AAA Series

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Guest Lecture "Deciding absorption"

Alexandr Kazda
Charles University, Prague

Date: Thursday, May 2
Time: 14:00
Room: S3 047 (JKU, Science Park 3)

The 4th Novi Sad Algebraic Conference & A Workshop on Semigroups and Applications

Novi Sad, Serbia, June 5-9, 2013

NSAC 2013  (Neues Fenster)
application/pdfFirst Announcement (169KB, Novi Sad, June 2013)

Thanks to the Constraint Satisfaction Problem, several new algebraic concepts
were discovered, among them the idea of absorption. If B is an absorbing
subalgebra of A, many kinds of connectivity properties of A are also true
for B. This makes absorption very useful for proofs by induction.

Unfortunately, we do not yet know how to algorithmically decide whether a given
subalgebra B of A is an absorbing subalgebra. In our talk, we will show one attempt to
provide such an algorithm: Assume we knew that B absorbs A iff there are
almost-Jónsson terms for B, and there are no blockers for B and A
(we leave the precise definitions for the talk). Since both of these conditions
can be checked algorithmically, we would have an algorithm that decides

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Guest Lecture "Algebraic approach to CSP and coloring by oriented trees"

Jakub Bulin
Charles University, Prague

Date: Friday, May 3
Time: 13:00
Room: S2 059 (JKU, Science Park 2)

Given a directed graph H, the H-coloring problem is the
following decision problem: input another digraph G and ask whether
there exists a homomorphism from G to H. The CSP dichotomy conjecture
of Feder and Vardi says that the H-coloring problem is always either
in P or NP-complete. The so-called algebraic approach to CSP, a link
of this combinatorial problem to universal algebra, has led to a
significant progress towards solving this conjecture and has brought a
new insight into some structural properties of digraphs. We will
present a few results and tools from this area and then apply them on
the case when H is an oriented tree. We will show that the CSP
dichotomy holds for a certain class of oriented trees, and discuss
possible directions for future research as well as related open

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Nik Ruskuc
University of St Andrews, Scotland

Date: Tuesday, March 26, 2013
Time: 13:00
Room: S3 057

Title: 1+1=2 makes direct products interesting

It is well known that the direct product of two groups G and H is finitely generated if and only if both G and H are finitely generated. But is this a theorem about: (a) groups; (b) classical, group-like algebraic structures (e.g. rings, associative algebras,...); (c) algebraic structures that naturally act on sets (i.e. semigroups); or (d) general algebraic structures? One can play the same game by replacing finite generation by other algebraic properties: finite presentability, decidable word problem, residual finiteness,... The answers differ from case to case, and a curious picture begins to emerge.

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85th Workshop on General Algebra
85. Arbeitstagung Allgemeine Algebra (AAA85)

Luxembourg, January 31 - February 2, 2013

AAA85 Luxembourg  (Neues Fenster)

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Das Doktoratskolleg "Computational Mathematics" stellt sich vor: Informationsveranstaltung für StudentInnen

Dienstag, 30. Oktober 2012
15:00 Uhr, K 269D

application/pdfInformationsveranstaltung für StudentInnen (142KB, 30.10.2012, 15:00 Uhr, K 269D)

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Startveranstaltung Mentoring Technische Mathematik

01. Oktober 2012, 15:30 - 17:00 Uhr, HS 6

Für den 01. Oktober 2012, 15:30-17:00 Uhr, HS 6 ist eine Informationsveranstaltung für StudienanfängerInnen der Studienrichtung Technische Mathematik geplant.

Unter dem Titel "Willkommen an der JKU - Informationen für Studierende der Technischen Mathematik" werden Peter Paule, RISC, Walter Zulehner, Vorsitzender der Studienkommission Technische Mathematik und Erhard Aichinger, Institut für Algebra in kurzen Vorträgen wichtige Informationen für StudienanfängerInnen bereitstellen. Die Vertreter der StV Mathematik werden ebenfalls anwesend sein.

ÖH StV Mathematik  (Neues Fenster)

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The Image of Mathematics – Mathematical Images August 27-31, 2012

Workshop for students, Internationale Akademie Traunkirchen

The Image of Mathematics  (Neues Fenster)

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LARD (The Linz Algebra Research Day)

June 21 at RISC, Schloss Hagenberg


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The 84th Workshop on General Algebra

Dresden, Germany, June 7-10, 2012

AAA series  (Neues Fenster)

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The 83rd Workshop on General Algebra & the 27th Conference of Young Algebraists

Novi Sad, Serbia, March 15-18, 2012


Former department member Mr. Peter Mayr, University of Lisbon, delivers plenary lecture at the 83rd Workshop on General Algebra.

Title of the lecture: Almost all finite semigroups are finitely related

AAA series  (Neues Fenster)

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