The objective of my research is to build novel quantum phases of matter and realize photonic control of chemical reactions using the emerging technology of ultracold polar molecules cooled to nanokelvin temperatures. Specifically, we will realize exotic topological superfluids built from interacting gases of polar molecules, which will feature extraordinary characteristics such as resistance to disorder, frictionless flow, and the emergence of strange “Majorana particles” that have never been detected in nature. Another complementary goal is to control chemical reactions built from the bottom up, molecule-by-molecule, by tailoring light-matter interactions of individual ultracold molecules coupled to an optical cavity. These capabilities will address fundamental questions relevant to condensed matter, atomic physics, and physical chemistry.