## 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.

Thursday, March 28, 2013 — 4:30 PM EDT

Thursday, March 28, 2013 — 3:30 PM EDT

This is a continuation from last week, in which I will prove the main theorem connecting idempotent strong Maltsev conditions satisfied by bipartite graphs, strongly bipartite digraphs, 2-sorted graphs, and structures with two equivalence relations.

Wednesday, March 27, 2013 — 4:30 PM EDT

Wednesday, March 27, 2013 — 2:30 PM EDT

We begin something new this week and I will give an overview of the theory of finitely generated subgroups of the group of invertible matrices over the complex numbers. In partic- ular, we will look at the so-called ”ping pong lemma”, which gives a strategy for showing that certain non-abelian subgroups of linear groups are in fact free groups.

Tuesday, March 26, 2013 — 4:30 PM EDT

Monday, March 25, 2013 — 4:00 PM EDT

We will discuss conformally flat complete Yamabe flow and show that in some cases we can give the precise description of singularity profiles close to the extinction time of the solution. We will also talk about a construction of new compact ancient solutions to the Yamabe flow.

Friday, March 22, 2013 — 3:30 PM EDT

Thursday, March 21, 2013 — 3:30 PM EDT

Wednesday, March 20, 2013 — 4:30 PM EDT

We will introduce 1-parameter groups of diffeomorphsims and associate them uniquely to compactly-supported vector fields. Using this idea, we will show, through an application of a Riemannian metric, that between consecutive critical points on a smooth manifold there exists only one diffeomorphism class. If we fail, we will face the horrors of chimney sweeping with Mr. Gamfield.

Wednesday, March 20, 2013 — 3:30 PM EDT

Triangular uniformly hyper-finite algebras are direct limits of triangular matrix algebras. I will talk about their isometric automorphism groups and dilation theory. In particular, we know what is the C*-envelope of the semidirect product of one of these algebras by an automorphism.

Please note: special time

Wednesday, March 20, 2013 — 3:30 PM EDT

We will describe an analytic framework that unites the analysis of the ASD equation with that of holomorphic curves. As an application, we will describe our approach to a version of the Atiyah-Floer conjecture relating the Floer homology groups of 3-manifolds defined by gauge theory to the groups defined by symplectic geometry.

Wednesday, March 20, 2013 — 2:30 PM EDT

This week we continue our look at solvable groups of subexponential growth. In particular, we will continue to look at the Milnor-Wolf theorem and the fact that an extension of two solvable-by-finite groups is again solvable-by-finite.

Tuesday, March 19, 2013 — 3:00 PM EDT

We will finish the proof of Theorem 2.33 and discuss some of its consequences and examples. Time permitting, we will introduce measures (from Chapter 7), which are generalizations of types, and discuss how the existent notions and theorems we saw for types can be generalized to measures.

Friday, March 15, 2013 — 3:30 PM EDT

Thursday, March 14, 2013 — 3:30 PM EDT

Abstract not available.

Wednesday, March 13, 2013 — 3:30 PM EDT

Wednesday, March 13, 2013 — 2:30 PM EDT

We continue our look at the theorem of Milnor and Wolf and will prove that a finitely generated solvable group of subexponential growth is nilpotent-by-finite. We will also look at solvable-by-finite groups.

Tuesday, March 12, 2013 — 3:30 PM EDT

We continue on products and Morley sequences of invariant types.

Tuesday, March 12, 2013 — 2:00 PM EDT

We consider Riemannian manifolds M with an isometric action by a Lie group G, for which the orbit space M/G is isometric to an orbifold. We compare G-invariant tensors on M with tensors on the orbifold M/G. The main ingredient is an algebraic result from the theory of symmetric spaces.

Special date, time and place.

Friday, March 8, 2013 — 3:30 PM EST

Thursday, March 7, 2013 — 3:30 PM EST

Wednesday, March 6, 2013 — 4:30 PM EST

I’m going to continue talking about the tangent spaces of a manifold. Given a smooth map f :M →N andapointp∈M,we’regoingtoconstructalinearmapfp :TpM →Tf(p)N -it’s this crazy thing you may have heard about before called the ’chain rule’. I will go through an explicit example or two in painstaking detail, and talk about why we care about points where this map has rank 0.

Wednesday, March 6, 2013 — 3:30 PM EST

Wednesday, March 6, 2013 — 2:30 PM EST

We'll continue our look at Gromov's theorem and consider the case of solvable groups. In particular, we will begin the proof that a finitely generated solvable group of polynomially bounded growth is nilpotent-by-finite. It is again my hope that the lecture will be accessible to a general audience.

Tuesday, March 5, 2013 — 3:30 PM EST

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