My research uses the tools of theoretical computer science to answer fundamental questions about the security of widely deployed cryptography. Much of my work focuses on the foundations of post-quantum cryptography, that is, classical cryptographic schemes that are secure even against an adversary with a quantum computer. This particular line of research has added urgency because such schemes are currently being standardized, with the goal of replacing much of our current (quantum-insecure) infrastructure in the near future. Specifically, my research focuses on the foundations of lattice-based cryptography, i.e., cryptography whose security relies on the presumed hardness of computational problems related to certain (beautiful) geometric objects called lattices. Lattices in fact have many additional applications in computer science and math (from algebraic number theory to error correction to complexity), and my work therefore also has broader applications.