# High Energy Physics Seminar

*,*Brookhaven National Laboratory

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As DUNE and T2HK ramp up their efforts, it is a good time to examine what the oscillation probabilities actually are. I will develop a framework for neutrino oscillations in matter that leads to simple and precise expressions. These expressions are sufficiently accurate for current, planned, and proposed oscillation experiments. Further improvements to these expressions can be derived via either changing the basis or perturbation theory, or both. While other expressions exist on the market, I will show how these expressions are significantly more precise and as simple. I will explore how ∆m2ee is modified in matter and how the previous techniques provide a simple and precise expression for this quantity as well. Finally, I will discuss recent results on understanding CP violation in the neutrino sector.