Applications of formal loop spaces and arc spaces

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I studied techniques and problems in algebraic geometry which are related to string theory, such as formal loop spaces and arc spaces. First, I obtained certain results on rationality of motivic zeta functions, which are certain functions obtained from the symmetric powers of varieties. An invariant, called nonstandard point counting, was introduced here. The structure of the totality of a string-theoretic variant of this invariant was studied. Also, I studied the contribution of a reducible curve to the relative Gromov-Witten invariant.