## 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, August 13, 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.

Tuesday, August 6, 2013 — 4:30 PM EDT

Tuesday, August 6, 2013 — 3:00 PM EDT

We take a break from NIP to talk about dp-minimality. I will use a 2011 paper by Dolich, Goodrick, and Lippel.

Tuesday, August 6, 2013 — 1:00 PM EDT

Hodge structure is an abstract notion modeled on the Hodge decomposition of cohomology groups of compact Kähler manifolds. We will introduce the basic notion of Hodge structure and see its relation with geometric objects such as abelian varieties and Riemann surfaces. If time permits we will discuss variation of Hodge structure, which is an important tool in complex algebraic geometry.

Tuesday, August 6, 2013 — 1:00 PM EDT

This talk will be a very brief summary of the work done up to date on a question posted by J.H.C. Whitehead in 1941. We will go through the statement of the conjecture, and review some classical results. Finally, we will use an algebraic characterization of 2-complexes to understand one of the approaches taken to solve the problem.

Friday, August 2, 2013 — 3:30 PM EDT

Friday, August 2, 2013 — 2:30 PM EDT

Mingzhong Cai recently introduced the degrees of provability to

compare the proof-theoretic strength of statements asserting the

totality of computable functions. They can also be viewed as the

Lindenbaum algebra of true $\Pi^0_2$ statements in first-order

arithmetic. We investigate the structure of the degrees of

Thursday, August 1, 2013 — 2:00 PM EDT

The main theme of this thesis is classifying classes of structures relative to various measurements. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on calculating the Turing ordinal and the back-and-forth ordinal of various theories, along with an exploration of how these two ordinals are related in general.

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.

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