Mathematical Sciences: Model Theory and Permutation Groups

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Thomas intends to use the methods of the theory of permutation groups to study omega-categorical expansions of infinite dimensional projective spaces over finite fields. In particular, he hopes to solve a special case of Lachlan's conjecture on stable omega-categorical structures. He also intends to use set theoretic techniques to solve problems about permutation groups and automorphism towers. Some of his methods have already led to a long-sought combinatorial design, which could be useful in the design of experiments.