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Are you tired of picking up the pieces when the robots on your  factory floor
collide?  Stumped by the way your protein chains manage to fold  themselves
up so quickly??  Stymied by how to combine the right chemicals in  your tiny
electrowetting pharmaceuticals lab??!  Look no further, the solution  is here:
state complexes.  They're cubical, they're non-positively curved, and  they'll
help you keep track of discretely moving objects.  They're also  subtle, but
with a little algebraic topology and discrete CAT(0) geometry we can  say a
good deal about them.  This talk will include some of what we know about
state complexes, some of what we'd like to know, reasons for caring  in the
first place, and a slew of pretty pictures.  Graduate students are  especially
welcome.
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