BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cheryl Praeger (University of Western Australia) DTSTART:20200623T120000Z DTEND:20200623T130000Z DTSTAMP:20260404T110645Z UID:Mathematics_Computer_Science/1 DESCRIPTION:Title: Mathematics of shuffling\nby Cheryl Praege r (University of Western Australia) as part of Colloquia Patavina\n\n\nAbs tract\nThe crux of a card trick performed with a deck of cards usually dep ends on understanding how shuffles of the deck change the order of the car ds. By understanding which permutations are possible\, one knows if a give n card may be brought into a certain position. The mathematics of shufflin g a deck of 2n cards with two “perfect shuffles” was studied thoroughl y by Diaconis\, Graham and Kantor in 1983. I will report on our efforts to understand a generalisation of this problem\, with a so-called “many ha nded dealer” shuffling kn cards by cutting into k piles with n cards in each pile and using k! possible shuffles.\nA conjecture of Medvedoff and M orrison suggests that all possible permutations of the deck of cards are a chieved\, as long as k is not 4 and n is not a power of k. We confirm this conjecture for three doubly infinite families of integers\, but the conje cture remains open. We initiate a more general study of shuffle groups\, w hich admit an arbitrary subgroup of shuffles.\nThis is joint work with Car men Amarra and Luke Morgan.\n\nCheryl Praeger is Emeritus Professor of Mat hematics at the University of Western Australia. In 2007 she won an Austra lian Research Council Federation Fellowship and in 2010-14 she served as i naugural Director of the Centre for the Mathematics of Symmetry and Comput ation at UWA. Her mathematical research work has transformed our understan ding of how groups act on large complex systems\, through new theories\, c onstructions\, algorithms and designs\, which exploit the classification o f the finite simple groups.\nProfessor Praeger received BSc and MSc degree s from the University of Queensland\, a DPhil degree from the University o f Oxford in 1973\, and has received honorary doctorates from Universities in six countries on three continents. She has served on the Executive of t he International Mathematical Union and on the Council and Executive of th e Australian academy of Science. She is a former Vice President of the Int ernational Commission for Mathematical Instruction\, and former Foreign Se cretary of the Australian Academy of Science. She is Fellow of the America n Mathematical Society\, an Honorary member of the London Mathematical Soc iety\, and she was the first woman to be President of the Australian Mathe matical Society of which she is now an Honorary Life Member. In 2019 she w as awarded the Prime Minister’s Prize for Science in recognition of her incredible contribution to mathematics research and education in Australia and around the world.\nProfessor Praeger has published more than 400 jour nal articles and five research monographs\, many of them with her students (30 PhD students\, 10 research masters students\, 21 postdoctoral researc h associates) and research colleagues. She has played an active role suppo rting and mentoring young scientists\, especially women.\n\nMore infos\nht tps://research-repository.uwa.edu.au/en/persons/cheryl-praeger\nhttps://en .wikipedia.org/wiki/Cheryl_Praeger\n LOCATION:https://stable.researchseminars.org/talk/Mathematics_Computer_Sci ence/1/ END:VEVENT END:VCALENDAR