I came dangerously close to claiming a false result at my talk on Monday. I didn't, but Alex's question at the end nailed an issue that nullifies a claim i'd had in my head following a written question by Thomas. Basically, while the intersection in the infinite Grassannian of a finite Schubert variety Xu and the affine Grassmannian itself is indeed (set-theoretically) the union of the affine Schubert varieties Xw with the core of w contained in the (homological) partition diagram of u. However, the full shuffles that i described, which are sufficient to cut out Xw when the shapes are the same, do not cut out from the matrix Schubert variety Yu the union of the matrix affine Schubert varieties of the various suitable w. It's because the vanishing minors aren't there to provide structural support (actually the antithesis, structural restrictions). I need to investigate this further.
Had i had my choice of undergrad, it'd've been Berkeley, and i'd've lived at a student co-op.
Brewed Awakening is an adorable shop along a surprisingly diverse and respectable strip of Euclid Ave. between Hearst and Ridge (happily smack between Jack's co-op and Bechtel (where the workshop is being held). They advertise having been voted "best place to study" in Berkeley, which says something about their location and the quality of their coffee . . . but i'm not quite sure what. But here today i learned something interesting about myself: The past two mornings i've not gotten a cookie with my mocha here because they'd cost $1.75, same as the muffins. This morning they were $1.60, so i figured "Why not?" (They're from a local bakery and one kind uses banana, chocolate, and walnut.) So i gave the barista two dollar bills. When he offered me my change, i motioned for him to keep it. O_o Make of that what you will, but keep in mind that i did it all without thinking.
Did i mention that i absolutely love living in a co-op? We need to found one in Blacksburg. This will be my mission if by some awful twist of fate (it would have to be) i end up living there indefinitely.
I have a very lively love/hate relationship with
Macaulay 2. That's all i'll say about that right now.