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SUMMARY:Israel Vainsencher (UFMG)
DTSTART:20201104T183000Z
DTEND:20201104T200000Z
DTSTAMP:20260423T021606Z
UID:BRAG/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BRAG/30/">En
 umerative geometry of legendrian foliations</a>\nby Israel Vainsencher (UF
 MG) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nFoliati
 ons\, or more generally\, distributions\, provide a geometric\nviewpoint i
 n the theory of differential equations. Grosso modo\,\na foliation of dime
 nsion one\, is a (polynomial) recipe to draw a line\nat each point. We’l
 l stick to 3-dim projective space. Similarly\, a\ndistribution of codimens
 ion one assigns a plane at each point. We\nassume the coefficients of the 
 equation of the plane are of degree one.\nAs syzygies trained minds will r
 ecognize\, this entails the distribution\nis specified by an anti-symmetri
 c 4×4 matrix. Those of maximal\nrank correspond to the distributions of c
 ontact. A foliation is called\nlegendrian whenever tangent to some distrib
 ution of contact. Our\ngoal is to describe the calculation of the dimensio
 n and degree of\nthe subvariety of legendrian foliations (and friends). It
  turns out that\nthe answer is given by Athus polynomials. This fits into 
 a Schubert\nCalculus like programme of exploring the geometry of parameter
 \nspaces of foliations.\n
LOCATION:https://researchseminars.org/talk/BRAG/30/
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