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SUMMARY:Vanishing cycle cohomology in geometry and representation theory
DTSTART:20250514T080000Z
DTEND:20250514T090000Z
DTSTAMP:20260513T134100Z
UID:indico-event-394@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ben Davison (The University of Edinburgh)\n\nGiven a
  regular function f on a smooth d-dimensional variety X\, as long as f is 
 in some sense generic\, we expect the critical locus of f to be zero-dimen
 sional\, since it can be described locally as the zero-locus of the d line
 arly independent partial derivatives of f. Many spaces S that arise natura
 lly in geometry\, topology and algebra are locally described as critical l
 oci of functions that are not\, however\, generic. This non-genericity is 
 actually good news\, reflecting the fact that these spaces are richer and 
 more interesting than disjoint unions of points.\nOne may assign a kind of
  "critical" Euler characteristic to such a space\, which heuristically cou
 nts the critical points of a generic deformation of f. While the tradition
 al Euler characteristic of a space can be defined as the alternating sum o
 f the dimensions of certain cohomology groups of that space\, this critica
 l Euler characteristic can be written as the alternating sum of the dimens
 ions of a different type of cohomology\, called vanishing cycle cohomology
 .\nI will introduce this cohomology theory\, along with a related cohomolo
 gy theory called BPS cohomology. This is a special finite-dimensional subs
 pace of the vanishing cohomology\, which generates it even when the critic
 al cohomology is infinite dimensional. These cohomology theories have many
  applications within geometry\, combinatorics and representation theory\, 
 which I will begin to describe.\n\nhttps://math-events.uni-bonn.de/event/3
 94/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/394/
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