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VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:GAAG seminar - Quadratic Segre indices: counting lines on hypersur
 faces over any field
DTSTART:20261028T141500
DTEND:20261028T160000
DTSTAMP:20261023T155925Z
UID:b4bd561ac83ce7431f07d553bcf44bda7662531a507c791e392814fa
CATEGORIES:Conferences - Seminars
DESCRIPTION:Felipe Espreafico Guelerman\nEvery smooth complex cubic surfac
 e contains exactly 27 lines\, but a real one may contain 3\, 7\, 15 or 27 
 real lines. Segre divided real lines into hyperbolic and elliptic ones\, d
 epending on whether a natural involution on the line has real fixed points
 . Assigning +1 to the elliptic lines and -1 to the hyperbolic ones\, the c
 ount is always 3. Kass and Wickelgren showed that this generalizes to a si
 ngle statement valid over any field: instead of signs\, each line contribu
 tes with a quadratic form over the field\, read off from its Segre involut
 ion. The total count is then the quadratic form 15〈1〉 + 12〈−1〉 i
 n the Grothendieck–Witt ring.\n\nIn this talk I will explain how this pi
 cture extends to lines on general hypersurfaces of degree 2n−1 in P^{n+1
 } for every n\, from the 27 lines on a cubic surface through the 2875 on a
  quintic threefold and beyond. Over the real numbers\, Finashin and Kharla
 mov attached to each line a Segre index\, built from involutions determine
 d by the secants of its Gauss curve. We show that a quadratic version of t
 his index computes the line’s local contribution to the A^1-Euler number
  over any perfect field of characteristic not 2. This generalizes the case
 s of cubic surfaces (Kass–Wickelgren) and quintic threefolds (Pauli). Th
 e real proof uses wall-crossing\, but ours is algebraic: a “conic model
 ” replaces the Gauss curve by a plane conic and a configuration of point
 s\, and the local index then factors as a product of resultants.\n\nThis i
 s joint work with Stephen McKean and Sabrina Pauli.
LOCATION:GR A3 32 https://plan.epfl.ch/?dim_floor=3&lang=en&dim_lang=en&tr
 ee_groups=centres_nevralgiques_grp%2Cmobilite_acces_grp%2Crestauration_et_
 commerces_grp%2Censeignement%2Cservices_campus_grp%2Cequipements_grp&tree_
 group_layers_centres_nevralgiques_grp=&tree_group_layers_mobilite_acces_gr
 p=metro&tree_group_layers_restauration_et_commerces_grp=&tree_group_layers
 _enseignement=guichet_etudiants&tree_group_layers_services_campus_grp=info
 rmation_epfl&tree_group_layers_equipements_grp=&baselayer_ref=grp_backgrou
 nds&map_x=2533184&map_y=1152531&map_zoom=15
STATUS:CONFIRMED
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