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DESCRIPTION: In the 19 th century\, cubic surfaces - defined by an implici
t equation of degree three in three variables - were among the first intere
sting examples in the development of modern algebraic geometry. A well-know
n result by Arthur Cayley and George Salmon is that any smooth cubic contai
ns exactly 27 straight lines. Other prominent facts are the classification
of all cubic surfaces w.r.t. their singularities by Ludwig SchlĂ¤fli\, and A
lfred Clebsch's birational map between the plane and such surfaces where si
x points play an essential role. The talk will present both the historica
l and the mathematical background of classical hand-crafted and also recent
3d-printed cubic surface models. Some of their fascinating features such a
s the movement of the straight lines as the surfaces vary may very well be
visualized using interactive software. In 2011 and 2014\, the speaker creat
ed two versions of a complete series of more than 45 types of 3d-printed cu
bic surface models. Copies of these are now part of several university coll
ections such as those at Lisbon\, Strasbourg\, Dresden\, and Mainz\, as wel
l as at the IHP at Paris. He will bring some examples of these sculptures w
ith him in order to illustrate facts which may better be appreciated when s
eeing and touching a real object.
DTSTAMP:20190201T100700
DTSTART:20190131T171500
CLASS:PUBLIC
LOCATION:HS 001/Arnimallee 3\n (Tea/coffee will be served from 16:45 in roo
m 006/A3.)\n
SEQUENCE:0
SUMMARY:Oliver Labs: Cubic Surface Models and their Historical and Mathemat
ical Background
UID:95960917@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/math/groups/ag-c/dates/31_01_2019_Labs.h
tml
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