The National Science Foundation Division of Mathematical Sciences awarded a $195,001 Project Grant to the University of Notre Dame under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The three-year award will support research into model-theoretic tree properties and their applications in algebra and combinatorics. Specifically, the Principal Investigator will continue developing the theory of model-theoretic tree properties and pursue applications of these properties in algebraic structures and combinatorial problems. The award also provides research training for graduate students. Model theory is a branch of mathematical logic focused on studying definable sets in mathematical structures. This research aims to isolate combinatorial features common to definable sets in tame structures and develop a general theory of structures satisfying these properties. Past work in this area has led to unification of concepts across fields and new insights in algebra and combinatorics through exploitation of structural similarities.