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12 Geometry and Topology
Geometry and Topology Speaker: Victor Turchin (Kansas State University) "Context free manifold calculus of functors and the operad of framed discs" Time: 15:30 Room: MC 107 Manifold calculus of functors was introduced and developed by T.
Goodwillie and M. Weiss in order to study spaces of embeddings. In a few
words the goal of their method is to understand how from the spaces
Emb(U,N) of smaller open subsets U of M we can describe the space Emb(M,N)
of embeddings of the entire manifold M into N. Naively it is sometimes
called "patching method". I will describe briefly the ideas of this theory
and also explain some recent advances which gives a connection with the
theory of operads. |
13 Pizza Seminar
Pizza Seminar Speaker: Seymour Ditor (Western) "Infinite Exponentials" Time: 16:30 Room: MC 107 When does an "infinite tower of exponentials" converge? To clarify, for positive real numbers a,b,… let us set Ea(x)=ax, and E(a,b,…,c)=Ea∘Eb∘⋯∘Ec(1), so E(a)=a, E(a,b)=ab, E(a,b,c)=abc. The question then is: for what sequences {an} of positive real numbers does the sequence {E(a1,…,an)} converge? |
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16 Algebra Seminar
Algebra Seminar Speaker: Lex Renner (Western) "The generic point of a group action" Time: 14:40 Room: MC 107 Starting with an action G×X→X
we analyze the maximal G-rational subalgebra
OK of k(X) and use it to obtain the
action GK×UK→UK where K=k(X)G, and UK is a certain quasi-affine variety over
K with O(UK)=OK. This gives us a generic "homogeneous" picture of the original action. We also analyze the maximal G-rational
subalgebra of k[X]p, where
p is a height-one G-prime of k[X].
We use these results to assess the behavior of
the canonical map π:U→U/G for
a sufficiently small G-invariant, open subset U of X. Finally we use observable G-actions over k to construct the functor K↦H1(K,G/H),
from finitely generated fields over k to Sets. From there we define the essential dimension of a homogeneous space G/H, whenever H⊂G is a
pair of connected, reductive groups.
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