BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yuveshen Mooroogen (University of British Columbia) DTSTART:20230420T150000Z DTEND:20230420T154000Z DTSTAMP:20260423T021931Z UID:QARF/10 DESCRIPTION:Title: La rge subsets of Euclidean space avoiding infinite arithmetic progressions\nby Yuveshen Mooroogen (University of British Columbia) as part of Queb ec Analysis and Related Fields Graduate Seminar\n\n\nAbstract\nAn arithmet ic progression (AP) is a collection of equally-spaced real numbers. It may be finite or countably infinite. It is known that if a subset of the real line has positive Lebesgue measure\, then it contains a k-term AP for eve ry natural number k. In joint work with Laurestine Bradford (McGill\, Ling uistics) and Hannah Kohut (UBC\, Mathematics)\, we prove that this result does not extend to infinite APs in the following sense: for each real numb er p in [0\,1)\, we construct a subset of the real line that intersects ev ery interval of unit length in a set of measure at least p\, but that does not contain any infinite AP. In this presentation\, I will explain the ge ometric features of our set that allow it to avoid such progressions. I wi ll also briefly discuss two recent preprints\, due to Kolountzakis-Papageo rgiou and Burgin-Goldberg-Keleti-MacMahon-Wang\, that were inspired by our work. These respectively employ probabilistic and topological methods\, i n contrast to our argument\, which relies on measure theory and equidistri bution of sequences mod 1.\n LOCATION:https://researchseminars.org/talk/QARF/10/ END:VEVENT END:VCALENDAR