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Quark Mixing Matrix Studies and Lepton Flavor Violation Searches Using Rare Decays of Kaons

I review recent results from experiments on rare decays of kaons, concentrating on searches for lepton flavor violation (LFV) and on measurements of quark mixing (CKM) matrix elements. The LFV results are the culmination of 15 years of experimentation at Brookhaven National Laboratory and are unlikely to be improved upon soon. The CKM studies derive from measurements of decay rates of charged and neutral kaons into lepton anti-lepton pairs, both with and without a charged or neutral pion. I discuss recent results and prospects for improved measurements that could provide an unambiguous test of the Standard Model explanation for CP violation. This paper is the written version of a talk presented at the Lepton-Photon Conference in August 1999.