the traveling salesman problem is one of the best-known examples of an algorithmically hard problem, but what does that mean formally? it turns out that a solution to this problem would immediately give a solution to any other np problem, and in this sense we say it is "np-complete." in this talk, we will give a more formal definition of what it means for a problem to be np-complete, develop the machinery needed to prove np-completeness, and then use this machinery to prove that the traveling salesman problem (and a few others) is indeed np-complete.

the springer resolution of the nilpotent cone of a semisimple lie algebra has important

applications in representation theory, and in particular was used by springer to give a geometric construction of the irreducible representations of weyl groups.  this talk concerns a generalization of the springer resolution constructed with the use of toric varieties.  we will discuss how this is connected in type a with lusztig's generalized springer correspondence, as well as an analogue of an affine paving of the fibers.  part of this talk is joint work with martha precup and amber russell.