Conditional decision problems and hunting algorithms in group theory.
by Maurice Chiodo
Abstract: Many interesting decision problems in group theory have been proven impossible, such as the word and isomorphism problems. However, one can investigate under what additional assumptions these problems are algorithmically solvable. In this talk we explore some of these problems, and check if they are solvable under tighter assumptions. One can rephrase some of these new problems in the context of topology as: "given a compact manifold and the knowledge that it is not simply connected, can we construct an essential loop?" or "given two compact manifolds and the knowledge that at least one is not simply connected, can we pick out such a case?".
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