BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Steven Robertson (University of Manchester) DTSTART:20241015T120000Z DTEND:20241015T130000Z DTSTAMP:20260423T021336Z UID:OWNS/138 DESCRIPTION:Title: L ow Discrepancy Digital Hybrid Sequences and the $t$-adic Littlewood Conjec ture\nby Steven Robertson (University of Manchester) as part of One Wo rld Numeration seminar\n\n\nAbstract\nThe discrepancy of a sequence measur es how quickly it approaches a uniform distribution. Given a natural numbe r $d$\, any collection of one-dimensional so-called low discrepancy sequen ces $\\{S_i : 1 \\le i \\le d\\}$ can be concatenated to create a $d$-dime nsional hybrid sequence $(S_1\, . . . \, S_d)$. Since their introduction b y Spanier in 1995\, many connections between the discrepancy of a hybrid s equence and the discrepancy of its component sequences have been discovere d. However\, a proof that a hybrid sequence is capable of being low discre pancy has remained elusive. In this talk\, an explicit connection between Diophantine approximation over function fields and two dimensional low dis crepancy hybrid sequences is provided. \n\nSpecifically\, it is shown that any counterexample to the so-called $t$-adic Littlewood Conjecture ($t$-L C) can be used to create a low discrepancy digital Kronecker-Van der Corpu t sequence. Such counterexamples to $t$-LC are known explicitly over a nu mber of finite fields by\, on the one hand\, Adiceam\, Nesharim and Lunnon \, and on the other\, by Garrett and the Robertson. All necessary concepts will be defined in the talk.\n LOCATION:https://researchseminars.org/talk/OWNS/138/ END:VEVENT END:VCALENDAR