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DTSTART:20181104T020000
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UID:calendar.103251.field_date.0@www.wpi.edu
DTSTAMP:20191211T085819Z
CREATED:20180529T140353Z
DESCRIPTION:Description of Event: \n\n\n\nQing Han\, Notre Dame\n\n\n\nTitl
e: The isometric embedding of abstract surfaces in the 3-dim Euclidean spa
ce\n\n\n\nAbstract: A surface in the 3-dim Euclidean space can be viewed a
s the image of a map from a planar domain to the 3-dim Euclidean space\, a
t least locally. The standard metric in the Euclidean space induces a metr
ic on the surface\, which allows us to compute the lengths of curves on th
e surface and to compute the distance of any two points on the surface. Fo
r example\, the distance of two points on a sphere is the length of the sm
all arc on the great circle through these two points. The induced metric o
n the surface can be transformed to an abstract metric by the abovemention
ed map. Now\, we consider the converse question. Given an abstract metric
on a planar domain\, can we find a surface in the 3-dim Euclidean space wh
ose induced metric is the given abstract metric? This is the isometric emb
edding problem we will discuss. It started with a conjecture by Schlaefli
in 1873 that this can always be achieved near any given point. This conjec
ture is widely open and there are only a few results under various conditi
ons. The question can be reformulated in terms of partial differential equ
ations. Despite the technical description\, the underlying equation has a
simple form. In this talk\, I will give a historical account and explain w
hy this equation is hard to solve. The talk is aimed at a general audience
.
DTSTART;TZID=America/New_York:20180907T110000
DTEND;TZID=America/New_York:20180907T120000
LAST-MODIFIED:20180904T133231Z
LOCATION:Stratton Hall
SUMMARY:Mathematical Sciences - Colloquium - Qing Han (Notre Dame)
URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
-colloquium-qing-han-notre-dame
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