BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gaurav Aggarwal (TIFR) DTSTART:20241203T171500Z DTEND:20241203T183000Z DTSTAMP:20260423T022037Z UID:NEDNT/81 DESCRIPTION:Title: S ingular matrices on fractals\nby Gaurav Aggarwal (TIFR) as part of New England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\n Abstract\nSingular vectors are those for which Dirichlet’s Theorem can b e improved by arbitrarily small multiplicative constants. Recently\, Klein bock and Weiss showed that the set of singular vectors has measure zero wi th respect to any friendly measure. However\, determining their Hausdorff dimension remains a subtle and challenging problem. Khalil addressed this by proving that the Hausdorff dimension of the set of singular vectors int ersecting a self-similar fractal is strictly smaller than the fractal’s dimension.\nIn this talk\, I will extend Khalil’s result in four key dir ections. First\, we generalize the study from vectors to matrices. Second\ , we analyze intersections with products of fractals\, such as the Cartesi an product of the middle-third and middle-fifth Cantor sets. Third\, we es tablish upper bounds for singular vectors in a generalized weighted settin g. Finally\, we derive an upper bound on the Hausdorff dimension of $\\ome ga$-very singular matrices in these broader settings\, extending earlier w ork of Das\, Fishman\, Simmons\, and Urbanski\, who studied the real\, unw eighted case.\nOur approach is dynamical in nature\, relying on the constr uction of a height function inspired by the work of Kadyrov\, Kleinbock\, Lindenstrauss\, and Margulis. This is a joint work with Anish Ghosh.\n LOCATION:https://researchseminars.org/talk/NEDNT/81/ END:VEVENT END:VCALENDAR