Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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We will see why C-minimal theories are dp-mininal, and hence conclude that the theory ACVF is NIP. We will also see why ACFA is ”not” NIP.
We consider the question of operator amenability of the $L^1$-algebra of a compact quantum group. In order to answer the question we instead look at a related concept of operator biflatness. The final result says for a
compact quantum group $G$, $L^1(G)$ is operator amenable if and only if $G$ is co-amenable and of Kac type, which excludes examples like
We will continue with the proof that the theory of algebraically closed valued fields has NIP. In the way we will talk about strongly dependent theories and dp-minimality.
We will discuss and give a proof of a special case of the Hodge conjecture: that for a smooth projective manifold, every (1,1) cohomology class is analytic. We will require some results from Kähler geometry, such as the Hodge-Dolbeault decomposition, which will be stated and their proofs sketched. If time permits we will make further remarks about the general Hodge conjecture.
For a set of numbers $A$, let the sum-set $A+A$ denote
We will take a step aside from Chapter 4 of Simon’s note, and jump the appendix to see why the theory of algebraically closed valued fields is NIP. Also, I will talk on why the model companion of difference fields is not NIP.
Let sq(n) denote the sum of the digits of a number n in base q. For example, s2(n) represents the number of 1s in the binary expansion of n. In 1978, Kenneth B. Stolarsky showed that lim inf n!1 s2(n2) s2(n)
= 0 using bounds obtained from analytical methods. In the last presentation we showed that the ratio s2(n2) s2(n) can indeed hit every positive rational number. In this presentation, we show that the same is
Suppose we have an algebraic group G acting algebraicly on a variety X, ie for each g ∈ G the associated map X → X is a morphism. A quotient of X by G is defined to be a variety Y and a morphism π : X → Y satisfying
(1) π−1(π(x)) = Gx for all x ∈ X.
(2) For any variety Z and G-invariant morphism X → Z, there is a unique factorization through Y.
Please note room and time.
We will continue on chapter 4 of the Pierre Simons notes. We will go further on mutually indiscernible sequences and start talking about DP-ranks.
Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on ”The Geometry of Yang-Mills Fields” by Sir Michael Atiyah. All are welcome to attend.
We finally finish the proof of Gromov’s theorem.
We will continue to go through section 2.2 of Pierre Simon’s notes. We will finish discussing our characterization of invariant 1-types in O-minimal theories and then discuss products and Morley sequences in O-minimal theories.
Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on "The Geometry of Yang-Mills Fields" by Sir Michael Atiyah.
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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