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SUMMARY:New techniques in resolution of singularities [MPIM]
DTSTART:20260409T130000Z
DTEND:20260409T140000Z
DTSTAMP:20260417T222600Z
UID:indico-event-1211@math-events.uni-bonn.de
DESCRIPTION:Speakers: Michael Temkin (The Hebrew University of Jerusalem/M
 PIM)\n\nMPI-Oberseminar\nSince Hironaka's famous resolution of singulariti
 es in characteristics zero in 1964\, it took about 40 years of intensive w
 ork of many mathematicians to simplify the method\, describe it using conc
 eptual tools and establish its functoriality. However\, one point remained
  quite mysterious: despite different descriptions of the basic resolution 
 algorithm\, it was essentially unique. Was it a necessity or a drawback of
  the fact that all subsequent methods relied on Hironaka's ideas essential
 ly?\nThe situation changed in the last decade\, when a logarithmic\, a wei
 ghted and a foliated analogues and generalizations were discovered in work
 s of Abramovich-Temkin-Wlodarzcyk\, McQuillan\, Quek\, Abramovich-Temkin-W
 lodarzcyk-Belotto and others. At this stage we can already try to figure o
 ut general ideas and principles shared by all these methods and the pictur
 e is quite surprising -- it seems that each method is quite determined by 
 its basic setting consisting of the class of geometric objects and basic b
 lowings up one works with. In particular\, the classical method is probabl
 y the only natural resolution (via principalization) method obtained by bl
 owing up smooth centers in the ambient manifold.\nIn my talk I'll describe
  the settings and the methods on a very general level. If time permits I w
 ill add some details about the simplest dream (or weighted) method\, which
  has no memory and improves the singularity invariant by each weighted blo
 wing up. Thus\, the algorithm becomes simplest possible and the (modest) p
 rice one has to pay consists of extending the setting of varieties (or sch
 emes) and blowings up of smooth centers to the setting of orbifolds and bl
 owings up weighted centers. \n \n\nhttps://math-events.uni-bonn.de/event
 /1211/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1211/
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