BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:João Nuno Mestre (University of Coimbra) DTSTART:20210312T130000Z DTEND:20210312T150000Z DTSTAMP:20260423T022843Z UID:DQSeminar/7 DESCRIPTION:Title: Some approaches to the differential geometry of singular spaces\nby João Nuno Mestre (University of Coimbra) as part of Deformation Quantizat ion Seminar\n\n\nAbstract\nSeveral objects that appear naturally in differ ential geometry - the zero set \nof a smooth function\, or the quotient of a manifold by a Lie group action\, for example - may not be smooth. \nBut we may still want to study their differential geometry\, to the extent po ssible\, in a way that generalizes \nusual concepts - the zero set of some functions\, and the quotient of some group actions are smooth\, we want \ nto generalize those.\n \nA few possible approaches are to take inspiratio n from algebraic geometry and study the object via an \nappropriately defi ned algebra\, or sheaf\, of smooth functions\; or maybe to decompose the o bject into smaller \npieces that are themselves smooth manifolds and fit t ogether nicely\; or to describe the object in kind of a \n"generators and relations" presentation\, where the generators and the relations are smoot h\, and work with the \npresentation instead. These lead us to the study o f differentiable spaces\, stratified spaces\, and Lie \ngroupoids (which g ive presentations for differentiable stacks).\n\nIn this introductory talk we will see the definitions of these concepts\, some examples in which th ey can be \nof use\, and some classes of singular spaces which are quite w ell behaved and have good descriptions in all \nthree pictures. I will als o try to mention a panoramic view of other approaches to singular spaces\, such as \ndiffeological spaces\, or noncommutative geometric techniques\, and how they relate to the examples presented.\n LOCATION:https://researchseminars.org/talk/DQSeminar/7/ END:VEVENT END:VCALENDAR