3:45PM: Tropical commutative algebraDiane MaclaganOne consequence of the recent push to develop a scheme theory in tropical geometry has been the development of a tropical commutative algebra. This starts with the commutative algebra of semirings, but in order to get a theory that interacts with geometry, we are lead to impose some combinatorial, matroidtheoretic, conditions. I will introduce these ideas, and discuss the current state of our understanding.

5:00PM: The Priddy Koszul complex and resolution of the residue field of a local ringDavid EisenbudLast week Mike Stillman spoke about recent investigations of Koszul algebras. I'll give some more general background on resolutions of the residue field of a local ring, and talk about work of Conca and others on bounds for the syzygies of a Koszul ring.
