Good locally testable codes

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• Alex Lubotzky (Weizmann Institute of Science)
• Thursday 24 July 2025, 13:30-14:20
• External.

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OGGW05 - Geometric and combinatorial methods in the foundations of computer science and artificial intelligence

An error-correcting code is locally testable (LTC) if a random tester 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). Based on joint work with I. Dinur, S. Evra, R. Livne, and S. Mozes. Fedor Pavutnitskiy Title: LLMs for the Working Mathematician Abstract: In this introductory talk I will survey foundational and recent works in the emerging area of using large language models (LLMs) in contemporary mathematical research. I will also discuss key challenges we have faced and share progress from our own ongoing projects. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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