## 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

Tuesday, July 31, 2012 — 10:00 AM EDT

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

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

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

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

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

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

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

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

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

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

This is a continuation of the previous talk.

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

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

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

Thursday, July 12, 2012 — 1:00 PM EDT

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.

Wednesday, July 11, 2012 — 3:40 PM EDT

Wednesday, July 11, 2012 — 1:00 PM EDT

Spiro Karigiannis, Pure Mathematics Department, University of Waterloo will speak on:

Abstract: I will discuss natural classes of connections on almost Hermitian manifolds, including the Bismut connection. I will be following closely the hard-to-find paper by Paul Gauduchon entitled "Hermitian Connections and Dirac Operators".

Tuesday, July 10, 2012 — 2:30 PM EDT

Abstract: We will begin this talk by introducing universal

specializations (section 2.2.1 in Zilber), which are specializations

that behave very nicely when extended further. We will then discuss

irreducible coverings (section 3.5.2), and begin to show that an

Tuesday, July 10, 2012 — 10:00 AM EDT

We have seen the outline of the circle method in Waring's

problem from Shuntaro's talks, where the minor arc contribution was

established by combining Weyl's inequality with Hua's lemma. In my two

talks, we will continue to see some improvements on minor arc estimates.

Thursday, July 5, 2012 — 3:30 PM EDT

The conjecture of Masser-Oesterl ́e, popularly known as abc-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures. This is a joint work with T. N. Shorey.

Thursday, July 5, 2012 — 1:00 PM EDT

We will see why a ring homomorphism A → B naturally induces a morphism (SpecB,OB) → (Spec A, OA) and why the converse is also true.

Wednesday, July 4, 2012 — 1:00 PM EDT

Benoit Charbonneau & Ren Zhu, Pure Mathematics, University of Waterloo

Wednesday, July 4, 2012 — 10:30 AM EDT

This is the fourth, and hopefully last, of several lectures in which I will describe an algorithm for problems whose constraints are cosets of subgroups of powers of a fixed group.

Tuesday, July 3, 2012 — 2:30 PM EDT

In this talk, we will introduce a broader definition of

pre-smoothness for general constructible sets, and discuss some

properties of pre-smooth sets. Time permitting, we will also look at

the specific case when the pre-smooth set is an algebraic curve.

University 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

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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.