Events

Omar Leon Sanchez, Pure Mathematics Department, University of Waterloo

“A couple of basic questions on ideals of K[x]”

Let K be a perfect field (i.e. K = Kp), L ≥ K and x an n-tuple of indeterminates. We will intensely look at the question: If I is radical in K[x], is IL[x] radical as well? As a consequence we will be able to answer the questions:

Adam Gutter, Pure Mathematics Department, University of Waterloo

"Zariski Structures: Non-Standard Analysis - Part II"

In this seminar, our focus is on introducing several new geometrically
motivated concepts, namely coverings, multiplicity, and local
functions. Time permitting, we may also discuss topological sorts, a
tool that allows us to generate new Zariski structures from a given
Zariski structure.

Theodore Hui, Pure Mathematics Department, University of Waterloo

“The Dynamics of the w Function”

Define P(x) the largest prime factor of x and let w(pqr)=P(p+q)P(p+r)P(q+r) for primes p,q,r. Then w maps the set A3 = pqr: not all equal to itself. It is also known that under the iteration of w, every element in A3 would eventually goes to the cycle 20,98,63,75. For any n ∈ A3, we use ind(n) to denote the least nonnegative integer i such that wi(n) ∈ 20,98,63,75.

Dennis The, Australian National University

"The gap phenomenon in parabolic geometries"

Many geometric structures (such as Riemannian, conformal, CR,
projective, systems of ODE, and various types of generic
distributions) admit an equivalent description as Cartan geometries.
For Cartan geometries of a given type, the maximal amount of symmetry
is realized by the flat model.  However, if the geometry is not

Spiro Karigiannis, Pure Mathematics, University of Waterloo

"Holonomy, G-structures, and intrinsic torsion"

We will start with a quick review of principal bundles and connections on both vector bundles and principal bundles. Then we will define the holonomy group of a connection and relate it to the parallel tensors on the manifold. We will also mention the Ambrose-Singer Theorem which relates the holonomy to the curvature of the connection.

Matilde Lalin, Université de Montréal

"Mahler measure of some K3-surfaces"

We study the Mahler measure of the three-variable Laurent
polynomial x+1/x+y+1/y+z-k where k is a parameter. The zeros of this
polynomial define (after desingularization) a family K3-surfaces. In
favorable cases, a singular K3-surface is obtained and the Mahler measure
is related to its L-function. This was first studied by Marie-Jose Bertin.

Julia Gordon, University of British Columbia

"The strange world of p-adic numbers"

This talk will be about the fields of p-adic numbers -- which, like the
real numbers, are completions of the rationals, but with respect to a
different metric -- the metric that  reflects divisibility by a prime p.
We will see some very strange effects caused by this unusual metric,  do

Ross Willard, Pure Mathematics Department, University of Waterloo

"Two problems at the intersection of universal algebra and logic"

Universal algebra has its roots in logic, and occasionally its problems approach the domain of logic. In this lecture I will explain two old open problems of this kind, both involving (incomplete) theories axiomatizable by equations.

Please note the time - regular time for Logic seminars will be 3:30pm.