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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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
We correct the argument from the last talk to prove that every formula has an honest definition.
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.
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.
We define honest definitions and give some examples.
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.
So far we have been studying a manifold M along with a smooth function f on M whose only critical points are nondegenerate. 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.
Fu, Li, and Yau proved the existence of balanced metrics on certain nonKahler manifolds which are obtained by conifold transitions of CalabiYau threefolds. In this talk, I will describe a result concerning the existence of HermitianYangMills connections on holomorphic vector bundles with respect to FuLiYau's metric.
We continue to investigate finitely generated subgroups of the general linear group and in particular when they contain free subgroups and free subsemigroups.
GuionnetJonesShlyakhtenko (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
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.
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.
We'll continue our look at linear groups and look at the socalled pingpong lemma, which is a tool used to prove the existence of free subgroups and free subsemigroups.
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Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca