The TREK program at J-PARC

The TREK program at J-PARC in Japan consists of a series of experiments that have been proposed to use the new, recently commissioned kaon beamline K1.1BR at the new J-PARC Hadron Facility. A beam of low-energy positively charged kaons will be stopped, and their decays observed with a large acceptance toroidal spectrometer capable of tracking charged particles with high resolution, combined with a photon calorimeter and additional instrumentation with muon polarimeters. The first two experiments, requiring less beam intensity, aim to test lepton universality in the $K_{e2}/K_{\mu2}$ ratio with 0.2\% statistical uncertainty, and to search for heavy sterile neutrinos in two-body kaon decays. Ultimately, the Time Reversal Experiment with Kaons (TREK) aims to find New Physics beyond the Standard Model by a precision measurement of the T-violating transverse polarization $P_T$ of muons in the $K^{+}_{\mu3}$ decay of stopped kaons with a sensitivity of $10^{-4}$. An overview of the planned experiments, results from recent R\&D activities, and the current project status will be presented.