Groups and Logic
何孟哲教授Purdue University 2:00 p.m. – 2:30 p.m. & 3:00 p.m. – 4:00 p.m. 鴻經館M107Abstract：
The interplay between group theory and logic had played a crucial role in both areas for many decades. One of the most famous questions in this intersection is the word problem proposed by Dehn in 1911. The word problem is shown to be unsolvable in general by Novikov in 1955. However, as a logician, the (un)solvability of a decision problem is only the beginning. For an unsolvable problem, computable structure theory gives a framework to study "how unsolvable" the problem is. On the other hand, for a solvable problem, formal language theory provides a way to study its complexity. We will survey various past and current results as well as some work in progress in these directions. We will also give some special attention to Gromov's model of random groups, and study the logical properties of them.
20191226演講_何孟哲教授 (Purdue University)