BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Semin Yoo (Institute for Basic Science\, Korea) DTSTART:20260717T130000Z DTEND:20260717T132500Z DTSTAMP:20260710T111632Z UID:CANT2026/59 DESCRIPTION:Title: Multiplicative irreducibility of shifted multiplicative subgroups\nb y Semin Yoo (Institute for Basic Science\, Korea) as part of Combinatorial and additive number theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nA central th eme in additive combinatorics is the interplay between addition and multip lication. Roughly speaking\, sets with strong multiplicative structure are not expected to exhibit rich additive structure\, and vice versa. In a re cent breakthrough\, Kalmynin resolved a conjecture of Lev--Sonn and Sárk özy on additive decompositions of multiplicative subgroups in prime field s and quadratic residues. Motivated by this work\, we study multiplicative analogues of these questions. We show that\, under a certain additional c ondition\, a shifted multiplicative subgroup cannot be written as a produc t set\, and that it also cannot be written as a ratio set unconditionally. In this talk\, I will discuss these results and the main ideas of the pro ofs. This talk is based on joint work with Seoyoung Kim (University of Bas el) and Chi Hoi Yip (Georgia Institute of Technology).\n LOCATION:https://researchseminars.org/talk/CANT2026/59/ END:VEVENT END:VCALENDAR