[Colloquium] Revised - Fernando Granha Candidacy Exam/Aug 30, 2021

[nitayack at uchicago.edu]

This is an announcement of Fernando Granha's Candidacy Exam.
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Candidate: Fernando Granha

Date: Monday, August 30, 2021

Time: 10 am CST

Remote Location: Zoom link: https://uchicago.zoom.us/j/99289631530?pwd=dUZzYnVGaGlIQ09vSXRoekZSWmNtQT09  Zoom password: 183271

Title: Bounds for Binary Codes

Abstract: A longstanding open problem in coding theory is to determine the best (asymptotic) rate $R(\delta)$ of binary codes with minimum (relative)
distance $\delta \in (0,1/2)$. On the existential side, the best result known is the Gilbert--Varshamov bound. On the impossibility side, 
McEliece, Rodemich, Rumsey and Welch gave the best upper bound known by analyzing linear programs of Delsarte and using properties of
orthogonal polynomials. To this date, there is still a substantial gap between these two bounds. We will discuss a few representative results
from the literature related to bounding $R(\delta)$ and possibly discuss some new directions.

Advisors: Madhur Tulsiani

Committee Members: Madhur Tulsiani, Janos Simon (Faculty Advocate), and Aaron Potechin