May 08, 2006 16:40
My review of the 83rd Peripatetic Seminar on Sheaves and Logic, in rec.juggling HLGCB style:
High: Francis Borceux's seminar on synthetic differential geometry (constructing infinitesimals by replacing the topos of sets with something more fancy) or Tom's four-line definition of Lebesgue integration. Both seriously cool. And the dinner at Balbir (on Church St) on the Saturday. Mmmmmm. So full....
Low: Probably the second session, when a combination of tiredness and post-talk adrenaline crash meant I could hardly follow anything.
Goals: not screw up my presentation (tick, on balance: it got a bit confusing at the end, and I probably spent too much time on the technical stuff and not enough on the conceptual side), understand derived categories (half-tick: I've got a bit of an idea, and that will hopefully improve when I go over my notes), understand semi-abelian categories (no tick there, alas), renew acquaintance with people from previous conferences and meet new ones (tick - and as an added bonus, the TA from my Game Semantics course at Oxford was there), have a good time (tick - though it was hella tiring)
Bane: Getting up in time for the start of lectures at 9am on a weekend :-( And the cat-herding involved in getting people to and from the various pubs and restaurants.
Oh, and that definition:
Let C be the category whose objects are triples (X, ξ, u), where X is a real Banach space, ξ:X ⊕ X → X is a bounded map, and u ∈ X with ||u|| ≤ 1, and whose morphisms are bounded Banach space homomorphisms X → X' preserving the ξ and u structure. Theorem/definition: the initial object of this category is (L1([0,1]), γ, 1), where γ is "juxtapose and squeeze", and the unique map !:(L1([0,1]), γ, 1) → (ℜ, mean, 1) is integration. Good, eh?
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