Connectionists: Western-Fields Seminar Series | Alex Lubotzky

[Lyle Muller]

The ninth talk in the 2021 Western-Fields Seminar Series in Networks, Random Graphs, and Neuroscience<http://www.fields.utoronto.ca/activities/21-22/western-fields> is next Thursday (11 November) at noon ET.

Alex Lubotzky (http://www.ma.huji.ac.il/~alexlub) will give a talk titled “The C^3 problem: locally testable codes with constant rate and constant distance” (abstract below). Dr. Lubotzky is Maurice and Clara Weil Chair in Mathematics at Hebrew University. Dr. Lubotzky completed his PhD under the supervision of Hillel Furstenberg (2020 Abel Prize) and has made foundational contributions in modern mathematics, ranging from group theory to number theory and graph theory. He is also one of the founders of the study of Ramanujan graphs.

This seminar series features monthly virtual talks from a diverse group of researchers across computational neuroscience, physics, and graph theory. We look forward to a talk from Jeannette Janssen (Dalhousie University) in December.

Registration link: https://zoom.us/meeting/register/tJYuf-GppzkjHt0W5HMDpME2UpUiE7ntO5JS

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An error-correcting code is locally testable (LTC) if there is a random tester that reads only a constant 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 2-dimensional objects seem to be of independent interest. The lecture will be self-contained.

Joint work with I. Dinue, S. Evra, R. Livne and S. Mozes

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Lyle Muller
http://mullerlab.ca

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