April 18, 2023: The Western Academy Welcomes Dr. Alex Lubotzky

Profile image of Dr. Alex Lubotzky, Weizmann Institute of Science and Hebrew University

Dr. Alex Lubotzky's research brings together coding theory and pure mathematics. Recently, Lubotzky collaborated with a team of computer scientists and mathematicians to devise a ground-breaking technique for testing communications for noise or unwanted distortions. These findings, which Quanta described as a "conceptual milestone," are among Lubotzky's many crucial contributions to mathematics and computer sciences. 

Lubotzky will be joining the Western Academy on Thursday, April 20th, to share his latest findings.

When: Thursday, April 20th, 4:45 pm EST
In-person: Middlesex College, Room 107
Zoom: https://westernuniversity.zoom.us/j/96923989092

Event title: Good locally testable codes


An error-correcting code is locally testable (LTC) if there is a random tester that reads only a small number of bits of a given word and decides whether the word is in the code, or at least close to it. A long-standing problem asks if there exists such a code that also satisfies the golden standards of coding theory: constant rate and constant distance. Unlike the classical situation in coding theory, random codes are not LTC, so this problem is a challenge of a new kind.

We construct such codes based on what we call (Ramanujan) Left/Right Cayley square complexes. These objects seem to be of independent group-theoretic interest. The codes built on them are 2-dimensional versions of the expander codes constructed by Sipser and Spielman (1996).
The main result and lecture will be self-contained. But we hope also to explain how the seminal work of Howard Garland ( 1972) on the cohomology of quotients of the Bruhat-Tits buildings of p-adic Lie group has led to this construction ( even though it is not used at the end).

Based on joint work with I. Dinur, S. Evra, R. Livne, and S. Mozes.