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SUMMARY:Arindam Biswas (Polynom Research\, Paris\, France)
DTSTART:20260716T130000Z
DTEND:20260716T132500Z
DTSTAMP:20260710T111542Z
UID:CANT2026/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/43/
 ">Asymptotic approximate groups in virtually nilpotent groups</a>\nby Arin
 dam Biswas (Polynom Research\, Paris\, France) as part of Combinatorial an
 d additive number theory seminar (CANT 2026)\n\nLecture held in Science Ce
 nter in the CUNY Graduate Center (4th floor).\n\nAbstract\nLet \\(G\\) be 
 a group and let \\(A\\subseteq G\\) be a non-empty subset. For\n\\(r\,l\\i
 n\\mathbb N\\)\, \\(A\\) is said to be an asymptotic\n\\((r\,l)\\)-approxi
 mate group if there exists \\(h_0\\in\\mathbb N\\) such that\,\nfor every 
 \\(h\\ge h_0\\)\, there is a set \\(X_h\\subseteq G\\) with\n\\(|X_h|\\le 
 l\\) and\n$A^{rh}\\subseteq X_hA^h.$\nWe study this property for subsets o
 f virtually nilpotent groups and show that\nevery finite non-empty symmetr
 ic subset of a virtually nilpotent group is an\nasymptotic approximate gro
 up. More generally\, the same conclusion holds for finite\nsets whose powe
 rs contain a symmetric word ball of radius comparable to \\(h\\). In the s
 etting of infinite sets\, we show a restricted nonabelian analogue of the 
 abelian semilinear-set theorem.\n
LOCATION:https://researchseminars.org/talk/CANT2026/43/
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