The tensor-like join: graph-theoretic insights into polar code performance Arikan's polar codes have been celebrated for their capacity-achieving performance since first presented in 2008; however, the question of optimal finite-length …

The introductory lecture is aimed at sharing background material so that students are better prepared to understand the main seminar. The introductory lecture is open only to students.

Higher Eisenstein Congruences  In this talk, we examine the relationship between the ``depth" of certain Eisenstein congruences and the local structure of the Eisenstein ideal. Specifically, let $latex p\geq 3$ …

The introductory lecture is aimed at sharing background material so that students are better prepared to understand the main seminar. The introductory lecture is open only to students.

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 …