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
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 ntuple 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. HeathBrown.
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 metatheorem on nsystems, and then we will look at an application of backandforth relations and nsystems.
Abstract:
We will continue our discussion of $n$systems, and prove a
general "metatheorem'' with a list of conditions that guarantee the
success of a priority construction.
This talk will be a continuation of the discussion in "part 1". There
are a few facts and definitions left to state before the local
consistency algorithm can be explained. Once this is all done, I will
define what it means for a structure to have bounded width, and prove
We say that $\{x,y,z\}$ forms a three term arithmetic progression
(or 3AP) if $x+z=2y$. For a finite abelian group $G$ we're interested in
finding the largest cardinality of all subsets $A\subseteq G$ with $A$
containing no 3APs. We denote this cardinality by $D(G)$. In this talk we
On an affine scheme Spec(R), a coherent sheaf is a sheaf that 'comes from a module' over R. In the case where S is a ($\mathbb{Z}$)graded ring, we may construct a graded Smodule out of S by 'twisting' the grading. This sheaf (over Proj(S)) is called O(1). I will go over some nonexamples of coherence, and go over the construction and basic properties of O(1).
Many constructions in computability theory are priority
arguments which build a c.e. set satisfying a list of requirements.
The complexity of such a construction can be measured by the
complexity of seeing how the requirements are satisfied, for example,
finite injury arguments are $\Delta_2$. We will introduce $n$systems,
a general method of formalizing such constructions which is useful
Consider a complex vector bundle $E$ over a manifold $M$. The
This is a continuation of the previous talk.
I will define what it means for a relational structure
$\mathbb{A}$ to have bounded width, and explain why such structures
are important. To do this, the local consistency algorithm has to be
explained, which requires several definitions about relational
structures. The actual definition of bounded width may spill into part
Abstract: We say that $\{x,y,z\}$ forms a three term arithmetic
progression (or 3AP) if $x+z=2y$. For a finite abelian group $G$ we're
interested in finding the largest cardinality of all subsets $A\subseteq
G$ with $A$ containing no 3APs. We denote this cardinality by $D(G)$.
In this talk we will prove a result of Lev's showing how $D(G)$ can be
bounded above based on the structure of the group $G$.
Abstract: Proj, coherence, and O(1) are all scary things in Hartshorne section II.5. I’ll do my best to explain them, and make them seem less scary.
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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.