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SUMMARY:Bernoulli Lecture II - Refined curve counting and tropical geometr
 y
DTSTART:20140515T150000
DTEND:20140515T160000
DTSTAMP:20260925T054159Z
UID:569517f831599f9797b5a992ccbdc3b3346bd6b10cb5b39b78e77f3b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Lothar Göttsche\nEnumerative geometry is a classical topic of
  algebraic geometry with many interesting connections to other parts of ma
 thematics\, but also to theoretical physics. Here we are concerned with en
 umerative geometry of curves on surfaces. A node of a curve is a transvers
 al self-intersection. The Severi degrees count degree d curves with a give
 n number of nodes in the projective plane through the appropriate number o
 f general points\, or more generally  in a linear system on a projective 
 surface.\nThe Welschinger invariants count the corresponding numbers of re
 al algebraic curves satisfying real point conditions. Both the Severi degr
 ees and the Welschinger invariants can also be computed in tropical geomet
 ry.\nUsing tropical geometry we  introduce refined Severi degrees\, Laure
 nt polynomials in  a variable y\, which interpolate between the Severi de
 grees\n(at y=1) and the Welschinger invariants (at y=1). After reviewing t
 he invariants\, we report on recent progress in studying these invariants\
 , e.g. relating them to refined Donaldson-Thomas invariants and progress t
 owards understanding the structure of their generating functions.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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