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BEGIN:VEVENT
DTSTART:20231110T220000Z
UID:175359@events.unl.edu
DTSTAMP:20230831T164949Z
ORGANIZER;CN=Jack Jeffries:
SUMMARY:Jack Huizenga\, Penn State University
STATUS:CONFIRMED
DESCRIPTION:Polynomial interpolation is an important subject in many areas
of mathematics\, from approximating functions in analysis and curve fittin
g in statistics to Hilbert functions in commutative algebra. The simplest
case is the problem solved by Lagrangian interpolation\, which discusses w
hen a single variable polynomial can have prescribed values at fixed point
s. Moving on\, when the polynomials have several variables\, the interpola
tion problem becomes much more challenging and depends heavily on the posi
tion of the points. For instance\, if 3 points are collinear\, then if we
know the values of a linear polynomial at two of the points then we also k
now it at the third.\n\nAfter introducing several basic interpolation prob
lems\, we will turn to studying the following problem. Given a collection
of $n$ points in the plane\, what is the most interesting codimension 1 pr
operty that those points can satisfy? For example\, it is one condition on
the coordinates of 3 points for them to lie on a line. We will phrase thi
s problem in terms of the computation of effective divisors on the Hilbert
scheme of points in the plane\, and see how a natural generalization of t
he polynomial interpolation problem provides the answer.
LOCATION:Avery Hall Room 115
URL://events.unl.edu/diversity/2023/11/10/175359/
DTEND:20231110T225000Z
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