Title: Statistical approach to tagging stellar birth groups in the Milky Way
Description: A major goal of the field of Galactic archeology is to understand the formation and evolution of the Milky Way disk. Stars migrate to different Galactic radii throughout their lifetimes, often leaving little dynamical signature of their initial orbits. Therefore, we need to look at the archaeological record preserved in stellar chemical compositions, which is indicative of their birth environment. In this thesis, we use the measurable properties of stars (chemical compositions and ages) to reconstruct the Milky Way disk's past. First, using hydrodynamical simulations, we find that a star's birth radius and age are linked to its chemical abundances. Subsequently, we learn that even with current-day measurement uncertainty and sample sizes, chemical abundances of Milky Way stars provide a route to reconstructing its formation over time. Extending the insights from hydrodynamical simulations to 30,000 stars observed across the Milky Way disk in the APOGEE survey reveals the importance of using the high-dimensional chemical abundance space.

Specifically, we determine that we can use groups of chemically similar stars with 19 measured abundances to trace different underlying formation conditions. Using the high-dimensional abundance data for 10,000 stars from two spectroscopic surveys, APOGEE and GALAH, we empirically describe the chemical abundance trends across a vast radial extent of the Milky Way disk. To do this, we employ a novel approach of quantifying radial variations for individual abundances conditioned on supernovae enrichment history. This enables us to assess the information content in each of the 15 abundances examined and capture the fine-grained signatures in the disk's chemical evolution history. This thesis outlines the potential of using stellar chemistry to trace different evolutionary events of the Milky Way disk, particularly in a time where survey data sample size and precision are growing rapidly.