BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gergely Kiss (Rényi Institute of Mathematics and Corvinus Univers ity\, Hungary) DTSTART:20260716T143000Z DTEND:20260716T145500Z DTSTAMP:20260710T111639Z UID:CANT2026/46 DESCRIPTION:Title: Lower bounds for mask polynomials with many cyclotomic divisors\nby Gergely Kiss (Rényi Institute of Mathematics and Corvinus University\, Hu ngary) as part of Combinatorial and additive number theory seminar (CANT 2 026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th fl oor).\n\nAbstract\nWe study finite subsets and multisets of cyclic groups \\(\\mathbb{Z}_M\\)\nwhose mask polynomials have prescribed cyclotomic div isors. More precisely\,\nif \\(A\\subseteq \\mathbb{Z}_M\\)\, we consider its mask polynomial $$\n A(X)=\\sum_{a\\in A} X^a\n \\qquad \\text{in } \\ mathbb{Z}[X]/(X^M-1)\,\n$$ and ask how divisibility by selected cyclotomic polynomials constrains\nthe size and structure of \\(A\\). \nThis questio n is motivated by its connections with translational tilings\,\nthe Coven- -Meyerowitz conjecture\, and one-dimensional Fuglede-type problems.\nWe pr ove new lower bounds for the cardinality of such sets and develop several\ nstructural tools\, including \\\\\n & a truncation method and a multiscal e extension of\nthe de Bruijn--Rédei--Schoenberg theorem. These results s how that the\nexpected fibre-type extremal configurations do not always gi ve the correct\nminimum once the prescribed cyclotomic divisors become suf ficiently complicated. \nAt the same time\, in the two-dimensional case an d in several further special\nsituations\, the lower bounds agree with the natural fibre constructions. This is joint work with I. Łaba\, C. Marsha ll\, and G. Somlai.\n LOCATION:https://researchseminars.org/talk/CANT2026/46/ END:VEVENT END:VCALENDAR