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#### Free semigroup algebras and the structure of an isometric tuple

(University of Waterloo, 2011-06-28)

An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ...

#### The Lang-Trotter conjecture for Drinfeld modules

(University of Waterloo, 2011-08-22)

In 1986, Gupta and Murty proved the Lang-Trotter conjecture in the case of elliptic curves having complex multiplication, conditional on the generalized Riemann hypothesis. That is, given a non-torsion point P∈E(ℚ), they ...

#### On the Erdös-Turán conjecture and related results

(University of Waterloo, 2011-08-29)

The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ...

#### A survey of Roth's Theorem on progressions of length three

(University of Waterloo, 2011-12-19)

For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=|A|/|B|. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer ...

#### Lower order terms of moments of L-functions

(University of Waterloo, 2011-06-17)

<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula ...

#### Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles

(University of Waterloo, 2011-08-10)

I will present the mean curvature flow in Euclidean spaces and the Lagrangian mean curvature flow. We will first study the mean curvature evolution of submanifolds in Euclidean spaces, with an emphasis on the case of ...