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Regular Seminar Minhyong Kim (University of Oxford)
Arithmetic geometry is the study *arithmetic schemes*, mathematical structures that have simultaneously an arithmetic and a geometric structure. The prototype is the so-called *spectrum of the integers* which is a geometric object on which the integers form the ring of functions. I will explain some of the difficult and classical problems that arise in their study, and how ideas of physics, especially topological quantum field theory, may be helpful.