Quot schemes and curve counting
-- Danny Gillam, April 29, 2011

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We will discuss the deformation, obstruction, and
intersection theory of the Quot scheme of a vector bundle on a
curve and explaing how this is related to sheaf theoretic curve
counting on local curves.  As time permits, we will discuss
relative versions of this Quot scheme where quotients are
required to be "well-behaved" near specified points of the
curve, so that they can be "glued".  Our approach uses
logarithmic geometry both to interpret "well-behaved" and to
keep track of vanishing cycles in degenerations.