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SUMMARY:The Challenges of Geometric Complexity Theory - Brgisser\, P (Tech
 nische Universitt Berlin)
DTSTART:20131017T090000Z
DTEND:20131017T100000Z
UID:TALK48234@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:It is a remarkable fact that two prominent problems of algebra
 ic complexity theory\, the permanent versus determinant problem and the te
 nsor rank problem\, can be restated as explicit orbit closure problems. Th
 is offers the potential for proving lower complexity bounds by relying on 
 methods from algebraic geometry and representation theory. This basic idea
  for the tensor rank problem goes back to work by Volker Strassen from the
  mid eighties. It leads to challenging problems regarding the irreducible 
 representions of symmetric groups over the complex numbers (tensor product
 s and plethysms).\n\nIn the first part of the talk\, we will present the g
 eneral framework\, explain some negative results\, and state some open pro
 blems. Then we will move on to outline some recent progress for proving lo
 wer bounds on the border rank of the matrix multiplication tensor. This is
  achieved by the explicit construction of highest weight vectors vanishing
  on the (higher secant) varieties of tensors of border rank at most r. \n\
 n
LOCATION:Seminar Room 1\, Newton Institute
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