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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The Challenges of Geometric Complexity Theory - Br
gisser\, P (Technische Universitt Berlin)
DTSTART;TZID=Europe/London:20131017T100000
DTEND;TZID=Europe/London:20131017T110000
UID:TALK48234AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48234
DESCRIPTION:It is a remarkable fact that two prominent problem
s of algebraic complexity theory\, the permanent v
ersus determinant problem and the tensor rank prob
lem\, can be restated as explicit orbit closure pr
oblems. This offers the potential for proving lowe
r complexity bounds by relying on methods from alg
ebraic geometry and representation theory. This ba
sic idea for the tensor rank problem goes back to
work by Volker Strassen from the mid eighties. It
leads to challenging problems regarding the irredu
cible representions of symmetric groups over the c
omplex numbers (tensor products and plethysms).\n\
nIn the first part of the talk\, we will present t
he general framework\, explain some negative resul
ts\, and state some open problems. Then we will mo
ve on to outline some recent progress for proving
lower bounds on the border rank of the matrix mult
iplication tensor. This is achieved by the explici
t construction of highest weight vectors vanishing
on the (higher secant) varieties of tensors of bo
rder rank at most r. \n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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