Distributed Storage Erasure codes, originally designed to provide reliability against noise on communication channels, are now widely used in distributed storage systems. Distributed storage systems require the codes to have …

Coded Computing Large-scale distribute computing frameworks such as MapReduce and Spark employ massive parallelization of jobs. While parallelism drastically reduces computation time, slow or straggling nodes can become a bottleneck in job …

Rateless Codes Rateless fountain codes are a class of erasure codes where the source generates an unlimited stream of symbols until the data is recovered at the receiver. This rateless property …

Solved and unsolved problems in additive number theory This will be a survey of recent results in combinatorial and additive number theory. The central object is the set of sums of …

On reductions from subset sum problem to shortest vector problem. The shortest vector problem (SVP) is a fundamental problem in lattice theory and its applications in cryptography. The hardness of SVP is …

Multivariate cryptography and Groebner bases -- Colloquium talk Multivariate cryptography is one of a handful of proposals for post-quantum cryptographic schemes, i.e., cryptographic schemes that are secure also against attacks …

Rank-metric codes and q-polymatroids Rank-metric codes are vector subspaces of the vector space of matrices of given size over a finite field, equipped with the distance function induced by the …

Universal Groebner bases and Cartwright-Sturmfels ideals Universal Groebner bases are systems of generators of ideals, which are a Groebner basis with respect to any term order. In this talk, I …

Jensen-Pólya Criterion for the Riemann Hypothesis and Related Problems In this talk, I will summarize forthcoming work with Griffin, Ono, and Zagier. In 1927 Pólya proved that the Riemann Hypothesis is equivalent …

NIST's Post-Quantum Cryptography Project (2012-2024) In recent years, there has been a substantial amount of research on quantum computers – machines that exploit quantum mechanical phenomena to solve mathematical problems …