## 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

**Fall term update:** visit our COVID-19 Information website for more information.

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

Wednesday, April 24, 2013 — 1:00 PM EDT

I give an overview of Bourgain’s argument in his 1989 paper, Bounded orthogonal systems and the Λ(p)-set problem. Through a rather complex argument, Bourgain was able to show, using elementary probabilistic methods, that for any 2 < p < ∞, almost every random set is Λ(p), where the mean density of the random sets is 2/p. Prior attempts at this problem

Wednesday, April 24, 2013 — 9:00 AM EDT

Tuesday, April 23, 2013 — 3:00 PM EDT

We correct the argument from the last talk to prove that every formula has an honest definition.

Wednesday, April 17, 2013 — 4:30 PM EDT

In this final talk of the term we will finish our discussion regarding the existence of Morse functions on manifolds in Euclidean space. In fact, as was teased at the end of the last talk, we will be able to find a very large number of such functions. This has some interesting applications, which we will also examine.

Wednesday, April 17, 2013 — 2:30 PM EDT

We have seen that Gromov's theorem for linear groups reduces to three claims. We will quickly recall these claims and then work on proving the last claim, which shows that under very general conditions that a linear group must have subexponential growth.

Tuesday, April 16, 2013 — 3:00 PM EDT

We define honest definitions and give some examples.

Friday, April 12, 2013 — 3:30 PM EDT

Using interpolation sets, we devise a fairly general method for estimating the size of quotients of function spaces on a locally compact group. This unifies approaches followed by many other authors (including us) to obtain particular cases. This is joint work with Jorge Galindo, University of Jaume I, Spain.

Thursday, April 11, 2013 — 3:30 PM EDT

Wednesday, April 10, 2013 — 4:30 PM EDT

So far we have been studying a manifold M along with a smooth function f on M whose only critical points are non-degenerate. We have made a lot of cool progress, but there is still a major hole: which manifolds actually admit these functions? I’m going to address this question when our manifold actually comes with an embedding into Euclidean space.

Wednesday, April 10, 2013 — 3:30 PM EDT

Fu, Li, and Yau proved the existence of balanced metrics on certain non-Kahler manifolds which are obtained by conifold transitions of Calabi-Yau threefolds. In this talk, I will describe a result concerning the existence of Hermitian-Yang-Mills connections on holomorphic vector bundles with respect to Fu-Li-Yau's metric.

Wednesday, April 10, 2013 — 2:30 PM EDT

We continue to investigate finitely generated subgroups of the general linear group and in particular when they contain free subgroups and free subsemigroups.

Friday, April 5, 2013 — 3:30 PM EDT

Guionnet-Jones-Shlyakhtenko (GJS) gave a diagrammatic proof of a

result of Popa which reconstructs a subfactor from a subfactor planar

algebra. In the process, certain canonical graded *-algebras with

traces appear. In the GJS papers, they show that the von Neumann

algebras generated by the graded algebras are interpolated free group

Thursday, April 4, 2013 — 3:30 PM EDT

A poset is said to be projective if its only idempotent polymorphisms

are projections. We will try to classify projective posets using

combinatorial properties. Projective posets of height 1 are completely

understood. Moreover, we know exactly when posets of height 1 have

Taylor polymorphisms. We will also discuss known results about posets

of greater height.

Thursday, April 4, 2013 — 2:30 PM EDT

I'll describe several new formulae for the Riemann zeta function, a few of which have application to high precision computation, and also discuss some unifying summation methods.

Wednesday, April 3, 2013 — 4:30 PM EDT

Wednesday, April 3, 2013 — 2:30 PM EDT

We'll continue our look at linear groups and look at the so-called ping-pong lemma, which is a tool used to prove the existence of free subgroups and free subsemigroups.

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