BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shahriar Mirzadeh (Michigan State University) DTSTART:20201120T171500Z DTEND:20201120T183000Z DTSTAMP:20260423T053140Z UID:NEDNT/10 DESCRIPTION:Title: O n the dimension drop conjecture for diagonal flows on the space of lattice s\nby Shahriar Mirzadeh (Michigan State University) as part of New Eng land Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbst ract\nConsider the set of points in a homogeneous space X=G/Gamma whose g_ t orbit misses a fixed open set. It has measure zero if the flow is ergodi c. It has been conjectured that this set has Hausdorff dimension strictly smaller than the dimension of X. This conjecture is proved when X is compa ct or when it has real rank 1. In this talk we will prove the conjecture f or probably the most important example of the higher rank case\, namely: G =SL(m+n\, R)\, Gamma=SL(m+n\,Z)\, and g_t = diag(exp(t/m)\, …\, exp(t/m) \, exp(-t/n)\, …\, exp(-t/n)). We can also use our main result to produc e new applications to Diophantine approximation. This project is joint wor k with Dmitry Kleinbock.\n LOCATION:https://researchseminars.org/talk/NEDNT/10/ END:VEVENT END:VCALENDAR