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:20260422T225637Z UID:Mathematics_Computer_Science/1 DESCRIPTION:Title: Mathematics of shuffling\nby Cheryl Praeger (Univ ersity of Western Australia) as part of Colloquia Patavina\n\n\nAbstract\n The crux of a card trick performed with a deck of cards usually depends on understanding how shuffles of the deck change the order of the cards. By understanding which permutations are possible\, one knows if a given card may be brought into a certain position. The mathematics of shuffling a dec k of 2n cards with two “perfect shuffles” was studied thoroughly by Di aconis\, Graham and Kantor in 1983. I will report on our efforts to unders tand a generalisation of this problem\, with a so-called “many handed de aler” shuffling kn cards by cutting into k piles with n cards in each pi le and using k! possible shuffles.\nA conjecture of Medvedoff and Morrison suggests that all possible permutations of the deck of cards are achieved \, as long as k is not 4 and n is not a power of k. We confirm this conjec ture for three doubly infinite families of integers\, but the conjecture r emains open. We initiate a more general study of shuffle groups\, which ad mit an arbitrary subgroup of shuffles.\nThis is joint work with Carmen Ama rra and Luke Morgan.\n\nCheryl Praeger is Emeritus Professor of Mathematic s at the University of Western Australia. In 2007 she won an Australian Re search Council Federation Fellowship and in 2010-14 she served as inaugura l Director of the Centre for the Mathematics of Symmetry and Computation a t UWA. Her mathematical research work has transformed our understanding of how groups act on large complex systems\, through new theories\, construc tions\, algorithms and designs\, which exploit the classification of the f inite simple groups.\nProfessor Praeger received BSc and MSc degrees from the University of Queensland\, a DPhil degree from the University of Oxfor d in 1973\, and has received honorary doctorates from Universities in six countries on three continents. She has served on the Executive of the Inte rnational Mathematical Union and on the Council and Executive of the Austr alian academy of Science. She is a former Vice President of the Internatio nal Commission for Mathematical Instruction\, and former Foreign Secretary of the Australian Academy of Science. She is Fellow of the American Mathe matical Society\, an Honorary member of the London Mathematical Society\, and she was the first woman to be President of the Australian Mathematical Society of which she is now an Honorary Life Member. In 2019 she was awar ded the Prime Minister’s Prize for Science in recognition of her incredi ble contribution to mathematics research and education in Australia and ar ound the world.\nProfessor Praeger has published more than 400 journal art icles and five research monographs\, many of them with her students (30 Ph D students\, 10 research masters students\, 21 postdoctoral research assoc iates) and research colleagues. She has played an active role supporting a nd mentoring young scientists\, especially women.\n\nMore infos\nhttps://r esearch-repository.uwa.edu.au/en/persons/cheryl-praeger\nhttps://en.wikipe dia.org/wiki/Cheryl_Praeger\n LOCATION:https://researchseminars.org/talk/Mathematics_Computer_Science/1/ END:VEVENT END:VCALENDAR