BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Linus Richter (Victoria University Wellington) DTSTART:20230130T200000Z DTEND:20230130T210000Z DTSTAMP:20260423T022712Z UID:CTA/89 DESCRIPTION:Title: Co- analytic Counterexamples to Marstrand’s Projection Theorem\nby Linus Richter (Victoria University Wellington) as part of Computability theory and applications\n\n\nAbstract\nA recent “point-to-set principle" of J. Lutz and N. Lutz characterises the Hausdorff dimension of any subset of Eu clidean space in terms of the complexity of its individual points. “Comp lexity" here refers to Kolmogorov complexity—so the point-to-set princip le gives us an algorithmic handle on classical problems in fractal geometr y: sets with particular fractal properties can now be constructed in stage s\, point-by-point\, by coding “enough” information into each point\, bit-by-bit.\nI will give a brief introduction to all these notions\, and p resent a new result in fractal geometry whose proof uses such effective me thods: under V=L\, I will outline the construction of co-analytic countere xamples to Marstrand’s Projection Theorem\, one of fractal geometry’s seminal theorems about the dimension of orthogonal projections of analytic plane sets onto lines. Our results also show that Marstrand’s theorem i s indeed sharp for analytic sets\, a fact previously unknown.\n LOCATION:https://researchseminars.org/talk/CTA/89/ END:VEVENT END:VCALENDAR