Joint Colloquium: Landsberg -- P vs NP and the geometry of orbit closures

Prof JM Landsberg (Texas A&M University) 

Friday 6th August, 2.35-3.25pm, Carslaw 175.  

P vs NP and the geometry of orbit closures 

Please note the unusual time.  This talk was originally announced as an algebra seminar;
instead Prof Landsberg will give an expository version of this talk in the colloquium
and speak on another topic in the algebra seminar.  We will leave for lunch from level 2
at 1 PM.  

L.  Valiant conjectured an algebraic variant of Cook's conjecture that the complexity
classes P and NP are distinct, where one instead compares the determinant and permanent
polynomials.  K.  Mulmuley and M.  Sohoni have proposed a program to prove Valiant's
conjecture using geometry and representation theory, which they call the Geometric
Complexity Theory (GCT) program.  I will give an overview of the GCT program, and
describe recent work with L.  Manivel and N.  Ressayre on the program, which led us to
solve a classical problem in algebraic geometry regarding dual varieties.  Independent
of complexity theory, the program has raised many new and beautiful questions regarding
the geometry of orbit closures, which I will discuss as time permits.