On Ferrers Diagram Codes Rank-metric codes play a crucial role in the area of random network coding. Mathematically, they are subspaces of a matrix space $latex \mathbb{F}^{m\times n}$ over a …

Coding Techniques for Partial Erasure Channels. Partial erasure channels were recently introduced to model erasure events in applications such as flash memories. In these channels, some information may remain after …

Efficient computations of bilinear pairings on elliptic curves over finite fields.  The Tate and Weil pairings play a vital role in computational number theory. For example, the Weil pairing can …

Code-based Cryptography for Post-Quantum Standardization In this talk, I will discuss some of the most recent developments in code-based cryptography and present the main candidates for NIST's post-quantum standardization call.

The Colmez Conjecture The Faltings height of an abelian variety is a fundamental invariant that was introduced in the proof of the Mordell conjecture.  Pierre Colmez formulated a conjectural interpretation …

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 …