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Events - June 2013

Friday, June 28, 2013 — 2:26 PM EDT

Robert Garbary, Pure Mathematics, University of Waterloo

“Jac(C) over any (perfect) field”

Thursday, June 27, 2013 — 3:30 PM EDT

Robert Garbary, Pure Mathematics, University of Waterloo

“More on Jac(C)”

Thursday, June 27, 2013 — 1:30 PM EDT

Vijay Patankar, ISI Chennai

“Intersective polynomials and Diophantine approximation”

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

Jason Bell, Department of Pure Mathematics University of Waterloo

“Gromov’s theorem XII: Kleiner’s theorem, continued”

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

Tuesday, June 25, 2013 — 3:00 PM EDT

Eeshan Wagh and Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo

“NIP Theories XV”

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

Xiaomei Zhao, Huazhong Normal University

“Diagonal behaviour in Vinogradov’s mean value theorem, Part II ”

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

Jordan Hamilton, Department of Pure Mathematics University of Waterloo

“Generalized Geometry: An Introduction”

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

David McKinnon, Pure Mathematics University of Waterloo

“Algebraic properties of Jacobians”

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

Jason Bell, Department of Pure Mathematics University of Waterloo

“Gromov’s theorem XI: Kleiner’s theorem, continued”

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

Tuesday, June 18, 2013 — 3:00 PM EDT

Eeshan Wagh and Christopher Hawthorne, Department of Pure Mathematics University of Waterloo

“NIP Theories XIV”

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

Matthew Beckett, Pure Mathematics, University of Waterloo

"The geometry of Yang-Mills fields, Part 05"

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

Xiaomei Zhao, Huazhong Normal University

“Diagonal behaviour in Vinogradov’s mean value theorem, Part I ”

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

Tyrone Ghaswala, Pure Mathematics University of Waterloo

“Jacobians - The Spice of Life”

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

Jason Bell, Pure Mathematics, University of Waterloo

"Gromov's theorem X: Kleiner's proof"

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

Ruizhang Jin, Pure Mathematics, University of Waterloo

"NIP XIII"

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

Tuesday, June 11, 2013 — 1:00 PM EDT

Tyrone Ghaswala, Pure Mathematics, University of Waterloo

"The geometry of Yang-Mills fields, Part 04"

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

Shuntaro Yamagishi, Pure Mathematics, University of Waterloo

"Sidon Problem in polynomial ring over finite field"

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

Tom Tucker, Rochester University

“Integral points in two-parameter orbits”

Thursday, June 6, 2013 — 11:55 AM EDT

Rahim Moosa, Pure Mathematics, University of Waterloo

“Abelian varieties as complex tori”

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

Rahim Moosa Department of Pure Mathematics University of Waterloo

“NIP Theories XII”

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

J C Saunders, Pure Mathematics Department, University of Waterloo

“Sums of Digits in q-ary expansions”

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)

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