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