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DTSTART:20190101T000000
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DTSTART;VALUE=DATE:20191104
DTEND;VALUE=DATE:20191109
DTSTAMP:20260609T161649
CREATED:20191015T180137Z
LAST-MODIFIED:20191128T011422Z
UID:4749-1572825600-1573257599@aarms.math.ca
SUMMARY:Surface Braid Groups and Mapping Class Groups
DESCRIPTION:Mini course by Professor Paolo Bellingeri Université de Caen \nSurface braid groups are a natural generalization of classical\nbraid groups and of fundamental groups of surfaces. They were first\ndefined by Zariski during the 1930’s (although braid groups on the\nsphere had been considered much earlier by Hurwitz)\, and they were\nre-discovered during the 1960’s in the study of mapping class groups and\nconfiguration spaces. These groups\, introduced as an “algebraic” tool\,\nturned out to be very difficult to understand. It is now common to use\nmapping class techniques to study the properties of surface braid groups. \nIn the last decade the interest in these groups grew notably\, in\nparticular due to their relations with knot theory and mapping class\ngroups and\, quite astonishingly\, with robotics. The mini course will\nstart with different definitions and group presentations for these\ngroups; this first part will allow us to present several combinatorial\nproperties\, such as residual properties\, central series\, and related\nquotients\, which will lead to some applications to finite type invariant\ntheory as well as linear and “symmetric” representations for surface\nbraid groups. We will then discuss the relation between surface braid\ngroups and mapping class groups. We will end with an overview on classic\nand more recent applications to knot theory in 3-manifolds. Here and\nthere we will present some open questions. \nThe lecturer of the mini course\, Paolo Bellingeri\, is a professor at the\nUniversity of Caen and the director of the Federation of Normandy\nLaboratories of Mathematics. He also serves as the lead scientist of the\nresearch group “Algèbre Représentations et Topologie pour l’Informatique\nQuantique et Classique” (ARTIQ). He has published widely on the topic of\nthe mini course and is one of the organizers of the conference series\n“WinterBraids” on this research area.
URL:https://aarms.math.ca/event/surface-braid-groups-and-mapping-class-groups-mini-course-by-professor-paolo-bellingeri-universite-de-caen/
LOCATION:Memorial University (St. John’s Campus)\, St. John's\, Newfoundland and Labrador\, Canada
CATEGORIES:AARMS workshops and conferences
ORGANIZER;CN="Yorck%20Sommerhauser":MAILTO:sommerh@mun.ca
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