Supported by the Paul Erdõs Summer Research Center of Mathematics

**Budapest, July 2--13, 2001**

SCIENTIFIC PROGRAM

The workshop will start on

July 2 (Monday) at 9 a.m.

and will conclude in the afternoon of July 13 (Friday). We expect that participants will arrive on July 1. The lectures will take place in the main lecture hall of the

Alfréd Rényi Mathematical Research Institute of the
Hungarian Academy of Sciences Address: Reáltanoda utca 13--15 Phone: 4838300 |

Here is a schedule of the program for the first week, which indicates the speakers and the topics they will discuss in their lectures:

**MONDAY**

9:00-- 9:10 Welcoming remarks

9:10--11:00 Keith Kearnes: local methods (part 1)

11:00--12:00 Problem session

12:00-- 2:00 Lunch break

2:00-- 4:00 Ágnes Szendrei: local methods (part
2)

4:00-- 5:00 Problem session

**TUESDAY**

9:00--11:00 Péter Pál Pálfy: minimal
algebras and the five types

11:00--12:00 Problem session

12:00-- 2:00 Lunch break

2:00-- 4:00 Pawel Idziak: the structure of <\alpha,\beta>-minimal
algebras

4:00-- 5:00 Problem session

**WEDNESDAY**

9:00--11:00 Ross Willard: term conditions

11:00--12:00 Problem session

12:00-- 2:00 Lunch break

2:00-- 4:00 Emil W. Kiss: the global influence of minimal
algebras

4:00-- 5:00 Problem session

**THURSDAY**

9:00--11:00 Ralph McKenzie: connections between the shape of
the congruence lattice and TCT properties

11:00--12:00 Problem session

12:00-- 2:00 Lunch break

2:00-- 4:00 Joel Berman: solvability

4:00-- 5:00 Problem session

**FRIDAY**

9:00--11:00 Ralph McKenzie: omitting types, Mal'tsev conditions

11:00--12:00 Problem session

12:00-- 2:00 Lunch break

2:00-- 4:00 Computer session: a demonstration of how computer
experimentation has led to new results in

tame congruence theory.

The following speakers have been asked to give talks during the second week: Joel Berman, Dejan Delic, Pawel Idziak, Keith Kearnes, Emil W. Kiss, Ralph McKenzie, Péter Pál Pálfy, Ágnes Szendrei, Matt Valeriote, Ross Willard, László Zádori. A schedule of lectures for the second week will be distributed during the workshop. During the first week there will be a course in tame congruence theory, and during the second week there will be lectures and discussion about areas of current research.

Our aim is to have the activities accessible to newcomers, yet interesting for all. It will be assumed that the participants are familiar with the basics of universal algebra (see, e.g. the material in the book by Burris--Sankappanavar, which can be downloaded from the page A Course in Universal Algebra).

ADDED LATER: SOME LECTURE NOTES

Lecture 1 + Exercises + Solutions

Lecture 2 + Exercises + Solutions

Lecture 6 + Exercises + Solutions

The status of the problems from the TCT book

ADDED LATER: PROGRAM FOR THE SECOND WEEK

**MONDAY**

9:00--10:00 Keith Kearnes: Examples

10:00--11:00 Péter Pál Pálfy: Congruence identities
in groups

11:00--12:00 László Zádori: Complexity problems
and finite algebras

12:00-- 2:00 Lunch break

2:00-- 3:00 Ágnes Szendrei: Classification problems

**TUESDAY**

9:00--10:00 Ross Willard: Interpretations and decidability

10:00--12:00 Matthew Valeriote: Decidability of finitely generated
varieties

12:00-- 2:00 Lunch break

2:00-- 4:00 Dejan Delic: Finite decidability of finitely
generated varieties

**WEDNESDAY**

9:00--11:00 Emil W. Kiss: Nilpotent and abelian algebras

11:00--12:00 Ágnes Szendrei: Minimal varieties

12:00-- 2:00 Lunch break

2:00-- 3:00 Keith Kearnes: Congruence identities -- an
application of subtraces

**THURSDAY**

9:00--10:00 Joel Berman: Free spectra

10:00--12:00 Pawel Idziak: G-spectra (part 1)

12:00-- 2:00 Lunch break

2:00-- 5:00 Ralph McKenzie: G-spectra (part 2)

**FRIDAY**

9:00--10:00 Matthew Valeriote: Residually small varieties (part
1)

10:00--11:00 Emil W. Kiss: Residually small varieties (part 2}

11:00--12:00 Keith Kearnes: Residually small varieties (part 3)

Last modified July 25, 2001