## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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Please note: The University of Waterloo is closed for all events until further notice.

Friday, June 28, 2013 — 2:26 PM EDT

Thursday, June 27, 2013 — 3:30 PM EDT

Thursday, June 27, 2013 — 1:30 PM EDT

Wednesday, June 26, 2013 — 2:30 PM EDT

We continue with Kleiner’s proof of Gromov’s thorem.

Tuesday, June 25, 2013 — 3:00 PM EDT

We will continue to go through section 2.2 of Pierre Simon’s notes. In particular, we plan on discussing invariant types, definability of types and Morley Sequences, and looking at examples in the O-minimal case.

Monday, June 24, 2013 — 11:30 AM EDT

In recent work of Ford and Wooley, considerable progress has been achieved in the diagonal behaviour in VMVT. In the first talk we discussed with the conjecture and best known results. In the second talk, we will sketch their proof of the main theorem.

Thursday, June 20, 2013 — 4:30 PM EDT

The study of both symplectic and complex geometry began hundreds of years ago, and have impacted many areas of mathematics and physics. Generalized complex geometry is a relatively new area of mathematics that encompasses both symplectic and complex geometry. In this talk we will examine some background of these areas and look at the structures on vector spaces and how they relate to each other.

Thursday, June 20, 2013 — 2:30 PM EDT

After Tys scintillating introduction to Jacobian varieties over the complex numbers, I will discuss the algebraic properties of Jacobians, with particular reference to number fields.

Wednesday, June 19, 2013 — 2:30 PM EDT

We continue with Kleiner’s proof of Gromov’s thorem.

Tuesday, June 18, 2013 — 3:00 PM EDT

We go over the material in section 2.2 of Pierre Simon’s notes again with an eye toward the o-minimal case.

Tuesday, June 18, 2013 — 1:00 PM EDT

Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on "The Geometry of Yang-Mills Fields" by Sir Michael Atiyah. All are welcome to attend.

Monday, June 17, 2013 — 11:30 AM EDT

In recent work of Ford and Wooley, considerable progress has been achieved in the diagonal behaviour in VMVT. We will begin my two talks with the conjecture and best known results in this front. In the remainder, we will sketch their proof of the main theorem.

Thursday, June 13, 2013 — 2:30 AM EDT

Given a genus g curve, we can associate an abelian variety to it called the Jacobian of the curve. Using the Riemann relations established last week, we will prove these Jacobians are indeed abelian varieties. Time permitting I will go into more depth regarding the case where g = 1.

The word Jacobian also occurs in vector calculus. Is this a coincidence? Rob thinks so.

Wednesday, June 12, 2013 — 2:30 PM EDT

Let G be a finitely generated group of polynomially bounded growth. We follow Kleiner's proof that G has an infinite homomorphic image with a faithful finite-dimensional representation. This is the main step of the proof.

Tuesday, June 11, 2013 — 3:00 PM EDT

We begin to chapter 4 (Dp-ranks) of Pierre Simon's notes.

Tuesday, June 11, 2013 — 1:00 PM EDT

Throughout the Spring 2013 term, we will (as a group) be reading through and lecturing on "The Geometry of Yang-Mills Fields" by Sir Michael Atiyah. All are welcome to attend.

Monday, June 10, 2013 — 11:30 AM EDT

Given a sequence of natural numbers $\omega$, we define $r_n(\omega) = | \{ (a,b) : a+b = n, a< b, \text{ and } a,b \in \omega \}|$. In 1954, Erdos proved that there exists a sequence $\omega$ such that $\log n \ll r_n(\omega) \ll \log n$. We consider the analogue of this question in polynomial ring over finite field.

Friday, June 7, 2013 — 2:30 PM EDT

Thursday, June 6, 2013 — 11:55 AM EDT

I will discuss how the complex points on an abelian variety have the structure of a complex torus. I will also discuss the Riemann-Hilbert relations which answer the question: When is a complex torus the complex points of an abelian variety?

Tuesday, June 4, 2013 — 3:00 PM EDT

We aim to complete chapter 3 of Pierre Simon’s notes.

Correction: time is 3:00 pm.

Monday, June 3, 2013 — 11:30 PM EDT

Let sq(n) denote the sum of the digits of a number n in base q. For example, s2(n) represents the number of 1s in the binary expansion of n. In 1978, Kenneth B. Stolarsky showed that

lim inf s2(n2) = 0 n→∞ s2(n)

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

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 Indigenous Initiatives Office.