# Events - 2012

Wednesday, August 15, 2012 — 1:00 PM EDT

## Geometry and Topology seminar

### 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

Thursday, August 9, 2012 — 4:00 PM EDT

## Student colloquium

### Theodore Hui, Pure Mathematics Department, University of Waterloo

#### “The Dynamics of the w Function”

Thursday, August 9, 2012 — 2:30 PM EDT

## Zariski Geometries working seminar

### 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.

Thursday, August 9, 2012 — 1:00 PM EDT

## Student Algebra seminar

### 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:

Wednesday, August 8, 2012 — 3:40 PM EDT

## Computability learning seminar

### Matthew Harrison-Trainor, Pure Mathematics University of Waterloo

#### “Pairs of computable structures”

Wednesday, August 8, 2012 — 3:09 PM EDT

## Constraint Satisfaction seminar

### Ian Payne, Pure Mathematics Department, University of Waterloo

#### “Determining CSP complexity using universal algebra”

Wednesday, August 8, 2012 — 1:00 PM EDT

## Geometry working seminar

### Li Chen & Jordan Rose, Pure Mathematics Department, University of Waterloo

#### Li Chen

##### "Symmetry groups of differential Equations Part III - Symmetry of differential equations with examples"
Tuesday, August 7, 2012 — 10:00 AM EDT

## Student Number Theory seminar

### Stanley Xiao, Pure Mathematics Department, University of Waterloo

#### "SOME RESULTS ON POWERFREE VALUES OF POLYNOMIALS IN ONE OR TWO VARIABLES"

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.

Thursday, August 2, 2012 — 2:30 PM EDT

## Zariski Geometries working seminar

### Adam Gutter, University of Waterloo

#### "Zariski Structures: Non-Standard Analysis"

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.

Wednesday, August 1, 2012 — 3:40 PM EDT

## Computability learning seminar

### Matthew Harrison-Trainor, Pure Mathematics, University Of Waterloo

#### "Pairs of computable structures"

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.

Wednesday, August 1, 2012 — 1:00 PM EDT

## Geometry working seminar

### Pure Mathematics Department, University of Waterloo

#### Matthew Beckett “Non-minimal Yang-Mills solutions”

Abstract:

Tuesday, July 31, 2012 — 10:00 AM EDT

## Student Number Theory seminar

### Xiaomei Zhao, Pure Mathematics, University of Waterloo

#### "New strategies for minor arc estimates: Part II"

Wednesday, July 25, 2012 — 3:40 PM EDT

## Computability learning seminar

### Matthew Harrison-Trainor, Pure Mathematics, University of Waterloo

#### "$n$-systems - Part II"

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.

Wednesday, July 25, 2012 — 1:00 PM EDT

## Geometry working seminar

### Jordan Hamilton, Pure Mathematics, University of Waterloo

#### Talk #1: "Generalized holomorphic bundles on Kodaira surfaces"

Wednesday, July 25, 2012 — 1:00 PM EDT

## Geometry working seminar - Part 2

### Li Chen, Pure Mathematics, University of Waterloo

#### Talk #2: "Symmetry groups of differential Equations Part II - Symmetry of algebraic equations"

Wednesday, July 25, 2012 — 10:30 AM EDT

## Constraint Satisfaction seminar

### Ian Payne, Pure Mathematics, University of Waterloo

#### "Bounded Width and the Local Consistency Algorithm: Part 2"

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

Tuesday, July 24, 2012 — 10:00 AM EDT

## Student Number Theory seminar

### Cassie Naymie, Pure Mathematics, University of Waterloo

#### "Lev's bounds for subsets containing no 3-APs (Part 2)"

We say that $\{x,y,z\}$ forms a three term arithmetic progression
(or 3-AP) 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 3-APs.  We denote this cardinality by $D(G)$. In this talk we

Thursday, July 19, 2012 — 1:00 PM EDT

## Student Algebra seminar

### Robert Garbary, Pure Mathematics, University of Waterloo

#### "Coherence and O(1)"

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 S-module out of S by 'twisting' the grading. This sheaf (over Proj(S)) is called O(1). I will go over some non-examples of coherence, and go over the construction and basic properties of O(1).

Wednesday, July 18, 2012 — 3:40 PM EDT

## Computability learning seminar

### Matthew Harrison-Trainor, Pure Mathematics, University of Waterloo

#### "$n$-systems"

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

Wednesday, July 18, 2012 — 1:00 PM EDT

## Geometry working seminar

### Tyrone Ghaswala, Pure Mathematics, University of Waterloo

Consider a complex vector bundle $E$ over a manifold $M$. The

Wednesday, July 18, 2012 — 1:00 PM EDT

## Geometry working seminar - Part 2

### Robert Garbary, Pure Mathematics, University of Waterloo

#### "Cherning butter into milk"

This is a continuation of the previous talk.

Wednesday, July 18, 2012 — 10:30 AM EDT

## Constraint Satisfaction seminar

### Ian Payne, Pure Mathematics, University of Waterloo

#### "Bounded Width and the Local Consistency Algorithm: Part 1"

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

Tuesday, July 17, 2012 — 10:00 PM EDT

## Student Number Theory seminar

### Cassie Naymie, Pure Mathematics Department, University of Waterloo

#### "Lev's bounds for subsets containing no 3-APs (Part 1)"

Abstract: We say that $\{x,y,z\}$ forms a three term arithmetic
progression (or 3-AP) 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 3-APs.  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 $G$.

Tuesday, July 17, 2012 — 2:30 PM EDT

## Zariski Geometries working seminar

### Adam Gutter, Pure Mathematics, University of Waterloo

#### "On elementary extensions of Zariski structures"

Thursday, July 12, 2012 — 1:00 PM EDT

## Student Algebra seminar

### David McKinnon, Pure Mathematics Department, University of Waterloo

#### "Proj, coherent sheaves, and O(1)"

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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