The document summarizes the TREK experiment at J-PARC, which aims to search for physics beyond the Standard Model by measuring the transverse muon polarization (PT) in stopped K+ decays. The TREK experiment plans to use an upgraded detector from the E246 experiment along with a new fiber target and GEM tracking chambers. It expects to achieve sensitivity to PT at the 10-4 level, allowing it to probe several theories of new physics. It will take data at the K1.1BR beamline at J-PARC, which has been commissioned for stopped kaon experiments and can provide the necessary 270 kW beam power for TREK's measurements when operating at full capacity in 2014.