A  COURSE  IN  TAME  CONGRUENCE  THEORY

WORKSHOP
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
During the first week there will be a course in tame congruence theory, and during the second week there will be talks about areas of current research.

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

Here are postscript files for some of the lectures given the first week.

Lecture 1 + Exercises + Solutions

Lecture 2 + Exercises + Solutions

Lecture 4 + Exercises

Lecture 5 + Exercises

Lecture 6 + Exercises + Solutions

Lecture 8 + Exercises

64 Problems

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