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SUMMARY:Good locally testable codes - Alex Lubotzky (Weizmann Institute of
  Science)
DTSTART:20250724T123000Z
DTEND:20250724T132000Z
UID:TALK234646@talks.cam.ac.uk
DESCRIPTION: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 whet
 her the word is in the code\, or at least close to it. A long-standing pro
 blem asks if there exists such a code that also satisfies the golden stand
 ards of coding theory: constant rate and constant distance. Unlike the cla
 ssical situation in coding theory\, random codes are not LTC\, so this pro
 blem is a challenge of a new kind. We construct such codes based on what w
 e 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 Sp
 ielman (1996). Based on joint work with I. Dinur\, S. Evra\, R. Livne\, an
 d S. Mozes. Fedor Pavutnitskiy Title: LLMs for the Working Mathematician A
 bstract: In this introductory talk I will survey foundational and recent w
 orks in the emerging area of using large language models (LLMs) in contemp
 orary mathematical research. I will also discuss key challenges we have fa
 ced and share progress from our own ongoing projects.&nbsp\;
LOCATION:External
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