3:45PM: Some basic homological constructionsDavid EisenbudIf you study representations (of a group or ring or...), the building blocks are the representations that are there "for free": the regular representation of a group, the free modules over a commutative ring,.... . The applications of representation theory are greatly extended by considering complexes and resolutions, and again there are some that are there "for free", such as the Koszul complex, whose definition actually goes back to Cayley. John Tate added to our store of such constructions with an important generalization of the Koszul complex. I'll describe some constructions that bear his name, leading to current work on that I have been doing with Frank Schreyer.

5:00PM: Degenerations and intersection theory in tropical and toric geometryChristopher EurThis is a expository talk for the tropical geometry student seminar. Continuing the theme of tropical compactifications from last time, we explore its flip side, degenerations. This can be viewed as the toric version of the usual Grobner degeneration in projective space over a valued field. We next give a brief overview of intersection theory through the lenz of tropicalization.
