Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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
In this trilogy of tales, we will meet three women who persevered
against all odds to leave a lasting mark on mathematics and
on future generations.
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.
The jump is an operator on sets with nice properties. It is
defined as the halting set relativized to oracles, but this
definition does not take into account how far we use the oracle. This
leads to the fact that some of these nice properties
do not hold for the bounded Turing reducibility, such as the
Schoenfield jump inversion. We will define another
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
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.
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:
In this talk I will discuss the problem of finding powerfree values of polynomials in one or two variables, with an emphasis on the determinant method of D.R. Heath-Brown.
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.
We will begin by finishing the proof of the meta-theorem on n-systems, and then we will look at an application of back-and-forth relations and n-systems.
Abstract:
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.