Borys Kuca

Recent developments in the polynomial Szemerédi theorem

The polynomial Szemerédi theorem of Bergelson and Leibman proves the existence of a broad class of polynomial patterns in large subsets of integers. Originally derived using soft methods of ergodic theory, it still awaits a quantitative proof that would yield an effective finitary statement. I will report on the recent progress towards this question and trace connections with ergodic theory and harmonic analysis.