Muon conversion — the process of a bound muon decaying into an energetic electron — is one of the best probes of charged lepton flavor violation. The experimental limit is soon expected to improve by four orders of magnitude, thus calling for precise predictions on the theory side. Equally important are precise predictions for muon decay-in-orbit, the main background for muon conversion. While the calculation of electromagnetic corrections to the two processes above the nuclear scale does not involve significant challenges, it becomes substantially more complex below that scale due to multiple scales, bound-state effects and experimental setup. In this talk, I present a systematic framework that addresses these challenges by resorting to a series of effective field theories. Combining Heavy Quark Effective Theory (HQET), Non-Relativistic QED (NRQED), potential NRQED, Soft-Collinear Effective Theory I and II, and boosted HQET, I derive a factorization theorem and present the renormalization group equations.

Neutrinos, though nearly massless and weakly interacting, play a central role in modern physics—from the origin of mass and the nature of matter–antimatter asymmetry to the search for physics beyond the Standard Model. Yet one of the main obstacles to fully realising their potential lies in our limited understanding of how neutrinos interact with matter. These interactions are complex, often involving nuclear effects that are difficult to model and challenging to measure. As a result, they introduce significant systematic uncertainties in precision experiments, including those aiming to determine mixing parameters and explore CP violation. This talk will provide an accessible overview of why neutrino interaction physics is both essential and challenging, and how it connects nuclear and particle physics. I will outline current experimental limitations and discuss the key requirements for future progress: well-characterised neutrino beams, dedicated measurements, and new experimental strategies. These advances are not only crucial for interpreting results from current and future experiments, but also for enabling discoveries that may reshape our understanding of fundamental physics. As an illustrative example, I will introduce nuSTORM—a proposed facility based on stored muons—as a next-generation platform for precision neutrino scattering and searches for new physics.

Optical atomic clocks with eighteen significant digits are the most accurate measurement devices available to us with applications ranging from tests of fundamental physics to height difference measurements in relativistic geodesy. The uncertainty in trapped-ion clocks is limited by systematic frequency shifts and quantum projection noise. In my presentation, I will show how quantum engineering techniques can overcome these limitations. Quantum algorithms provide access to new clock species such as highly charged ions with reduced systematic shifts and high sensitivity to searches for new physics, including hypothetical fifth forces, variation of fundamental constants and dark matter candidates. Dynamical decoupling and entangled state spectroscopy in a multi-ion frequency reference offer suppression of systematic shifts, while improving the signal-to-noise ratio of the clock and thus the required averaging time to reach a certain resolution. These developments will pave the way towards a next generation of quantum-enhanced clocks that enter the 10-19 relative frequency uncertainty regime.