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SUMMARY:Counting inscribed geometric objects
DTSTART:20260915T080000Z
DTEND:20260915T090000Z
DTSTAMP:20260915T102400Z
UID:indico-event-17312@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Polyak\n\nEnumerative geometric problems de
 al with counting geometric objects in a special position relative to anoth
 er object and naturally appear in a number of fields. Simple examples in l
 ow-dimensional geometry include\, for example\, a celebrated Toeplitz' sq
 uare peg problem\, or Pannwitz' and Denne's results on knot quadrisecants.
  In algebraic geometry one counts algebraic curves of a fixed degree and g
 enus satisfying various passage/tangency conditions. As usual in real geo
 metry\, in order for such numbers to be locally constant\, one has to coun
 t the corresponding objects with certain signs. Corresponding signs are n
 ot always easy to find (in some cases they remain mysterious) and even gi
 ven these signs\, proving that the total signed count is invariant under 
 small deformations can be tedious. I will discuss a number of various cou
 nting problems\, including triangles inscribed in planar curves\, bitange
 nts and binormals of planar curves\, characteristic bitangents of immersed
  hypersurfaces\, and various secants of knots and links. All of them allow
  for a similar treatment based on maps of configuration spaces and the i
 ntersection theory.\n\nhttps://indico.math.cnrs.fr/event/17312/
LOCATION:125 (Braconnier)
URL:https://indico.math.cnrs.fr/event/17312/
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