ABSTRACT: Lattices are fundamental objects that have many applications in computer science, including to optimization, cryptanalysis, robust communication, and especially the design of secure cryptography. In particular, lattices are essential to post-quantum cryptography---cryptography that is apparently secure even against quantum adversaries. The National Institute of Standards and Technology (NIST) recently standardized several lattice-based cryptosystems, and these schemes will very likely be in widespread use soon. So, it is crucial to understand their security in detail as soon as possible.

In this talk, I will discuss recent work on the computational problems underlying lattice-based cryptography, focusing on the following directions:

1. The complexity of lattice problems.

2. Connections between lattices and error-correcting codes.

3. The problem of deciding whether two lattices are "essentially the same."

BIO: Huck Bennett is an assistant professor at the University of Colorado Boulder. His research area is theoretical computer science, with an emphasis on lattices, error-correcting codes, fine-grained complexity, and algebraic and geometric algorithms. Before Colorado, he was an assistant professor at Oregon State University for 2.5 years, and before that he did postdocs at the University of Michigan and Northwestern University. He graduated with his Ph.D. from the Courant Institute of Mathematical Sciences, New York University in 2017 advised by Daniel Dadush and Chee Yap.