Odd symmetric functions and odd categorifed quantum sl(2)

We introduce odd analogues of the symmetric functions, the nilHecke algebra, and the cohomology of Grassmannians. These algebras are used in constructing an odd categorification of quantum sl(2) and, conjecturally, odd Khovanov homology. By work of Hill and Wang, there is a relation to the categorification of Kac-Moody superalgebras as well. Joint with Mikhail Khovanov and Aaron Lauda.