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DTSTART;TZID=America/Toronto:20231130T133000
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URL:https://uwaterloo.ca/pure-mathematics/events/special-colloquium-51
SUMMARY:Special Colloquium
CLASS:PUBLIC
DESCRIPTION:XUJIA CHEN\, HARVARD UNIVERSITY\n\n\"WHY CAN KONTSEVICH'S INVAR
 IANTS DETECT EXOTIC PHENOMENA?\"\n\nIn topology\, the difference between 
 the category of smooth manifolds\nand the category of topological manifo
 lds has always been a delicate\nand intriguing problem\, called the \"exot
 ic phenomena\". The recent work\nof Watanabe (2018) uses the tool \"Kontse
 vich's invariants\" to show\nthat the group of diffeomorphisms of the 4-d
 imensional ball\, as a\ntopological group\, has non-trivial homotopy type.
  In contrast\, the\ngroup of homeomorphisms of the 4-dimensional ball is c
 ontractible.\nKontsevich's invariants\, defined by Kontsevich in the early
  1990s from\nperturbative Chern-Simons theory\, are invariants of (certai
 n)\n3-manifolds / fiber bundles / knots and links (it is the same argument
 \nin different settings). Watanabe's work implies that these invariants\nd
 etect exotic phenomena\, and\, since then\, they have become an\nimportant
  tool in studying the topology of diffeomorphism groups. It\nis thus natu
 ral to ask: how to understand the role smooth structure\nplays in Kontsevi
 ch's invariants? My recent work provides a\nperspective on this question: 
 the real blow-up operation essentially\ndepends on the smooth structure\,
  therefore\, given a manifold / fiber\nbundle X\, the topology of some ma
 nifolds / bundles obtained by doing\nsome real blow-ups on X can be differ
 ent for different smooth\nstructures on X.\n\nZoom\nlink: https://uwaterl
 oo.zoom.us/j/2433704471?pwd=aXJoSDh0NDF0aFREbkthSnFBOUI4UT09
DTSTAMP:20260505T152519Z
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