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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Speaker: Raghu Meka (UCLA)\n\nTitle: Strong bounds for 3-pro
gressions\n\nAbstract:\n\nSuppose you have a set S of integers from \{1\,2\
,...\,N \ that contains at least N / C elements. Then for large enough N \,
must S contain three equally spaced numbers (i.e.\, a 3-term arithmetic pr
ogression)?\n\nIn 1953\, Roth showed that this is indeed the case when C >
\Omega(\log \log N)\, while Behrend in 1946 showed that C can be at most 2^
{O(\sqrt{\log N})}. Since then\, the problem has been a cornerstone of the
area of additive combinatorics. Following a series of remarkable results\,
a celebrated paper from 2020 due to Bloom and Sisask improved the lower bou
nd on C to C = (\log N)^{1+c}\, for some constant c > 0.\n\nThis talk will
describe a new work that C >2^{\Omega((\log N)^{0.09)\, thus getting closer
to Behrend's construction. Based on joint work with Zander Kelley.\n\nThe
first hour of the talk will be self-contained and describe the main ideas o
f the proof. The second hour will be a deeper follow-up of some elements of
the proof.
DTEND:20230322T210000Z
DTSTAMP:20230926T233455Z
DTSTART:20230322T190000Z
LOCATION:MIT-Math Dept.\, Room 2-449
SEQUENCE:0
SUMMARY:Joint TCS - Combinatorics Seminar
UID:tag:localist.com\,2008:EventInstance_42715697477491
URL:https://calendar.mit.edu/event/joint_tcs_-_combinatorics_seminar
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