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Thursday, January 28, 2016

**Abstract:** Over the past few decades, Feynman integrals have been studied extensively in order to formulate the standard model of particle physics (i.e., the theory explaining how fundamental particles interact). In certain cases, these integrals can be expressed as periods associated to algebraic varieties and are conjectured to encode some interesting arithmetic information about the varieties. More precisely, numerical evidence suggests that their evaluations are, up to simple factors, special values of $L$-functions. In this talk, we will briefly explain what Feynman integrals are and present a recent result on Feynman integral evaluations related to critical values of $L$-functions of $K3$ surfaces, which was discovered numerically by D. Broadhurst.