## 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

**University COVID-19 update:** visit our Coronavirus Information website for more information.

Please note: The University of Waterloo is closed for all events until further notice.

Tuesday, July 30, 2013 — 3:00 PM EDT

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.

Tuesday, July 30, 2013 — 2:30 PM EDT

Tuesday, July 30, 2013 — 1:00 PM EDT

Monday, July 29, 2013 — 11:30 AM EDT

Friday, July 26, 2013 — 3:30 PM EDT

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

Tuesday, July 23, 2013 — 3:00 PM EDT

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.

Tuesday, July 23, 2013 — 1:00 PM EDT

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.

Monday, July 22, 2013 — 11:30 AM EDT

For a set of numbers $A$, let the sum-set $A+A$ denote

Friday, July 19, 2013 — 3:30 PM EDT

Thursday, July 18, 2013 — 3:30 PM EDT

Tuesday, July 16, 2013 — 3:00 PM EDT

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.

Monday, July 15, 2013 — 11:30 PM EDT

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

Thursday, July 11, 2013 — 2:30 PM EDT

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.

Thursday, July 11, 2013 — 1:15 PM EDT

Please note room and time.

Tuesday, July 9, 2013 — 3:00 PM EDT

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.

Tuesday, July 9, 2013 — 1:00 PM EDT

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.

Monday, July 8, 2013 — 11:30 AM EDT

Thursday, July 4, 2013 — 3:30 PM EDT

Wednesday, July 3, 2013 — 2:30 PM EDT

We finally finish the proof of Gromov’s theorem.

Tuesday, July 2, 2013 — 3:00 PM EDT

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.

Tuesday, July 2, 2013 — 1:00 PM EDT

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.

University 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

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1