The Seminar on Discrete Mathematics and Algebra is an informal group of mathematicians working at the Department of Mathematics of the Faculty of Physics, Mathematics and Optometry of the University of Latvia under the leadership of Professor Jānis Buls. The following dissertations have been defended in this framework:

Algorithm theory was developed in the 1930s with the contribution of Alonzo Church, Alan Turing and other mathematicians. The modern computer is an implementation of this theory (universal Turing machine). In the late 1940s, Emil Post and Andrey Markov independently proved that the problem of words in semigroups is generally algorithmically undecidable. This is the first proven problem in classical mathematics for which there is no algorithm.

Later, Pyotr Novikov proved that the uniform word problem is also undecidable. In the 1960s, systematic research was started in connection with machine (automaton) semigroups, and later also with groups. It was only in 2013 that Pierre Gillibert proved that the finite problem in automaton subgroups is algorithmically undecidable. Solution of an analogical problem in automaton groups is still a challenge. The Seminar on Discrete Mathematics and Algebra addresses this set of topics.

Participants of the group – Insa Krēmere, Līga Užule, Raivis Bēts, Aigars Valainis, Jiri Janda, Jānis Cīrulis, Sandra Ose un Meldra Romanovska.

 

janis.buls@lu.lv