Improved lower bounds for Szemeredi’s theorem.

Add to your list(s) Download to your calendar using vCal

• Zach Hunter (ETH Zurich)
• Thursday 19 October 2023, 14:30-15:30
• MR12.

If you have a question about this talk, please contact ibl10.

Let $r_k(N)$ denote cardinality of the largest subset of $\{1,…,N\}$ which does not contain an arithmetic progression of length $k$. Since 1961, the best lower bound (up to lower order terms) has been due to Rankin, establishing $r_k(N) \ge N exp(-(c_k+o(1)) \log^{p_k}(N))$ for certain explicit constants $c_k,p_k> 0$, generalizing a construction of Behrend.

We shall establish new bounds for this problem, improving the constant $c_k$ for all $k\ge 7$ (with the same value of $p_k$). Our methods also have implications for related problems in finite fields.

This talk is part of the Combinatorics Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• Combinatorics Seminar
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.