Wednesday, June 13, 2017

3:10 p.m.

BA6183

PhD Candidate: James Lutely

Supervisor: Georges Elliott

Thesis title:

******

Abstract:

A copy of the thesis can be found here:

]]>*Wednesday, June 7, 2017
*

*3:10 p.m.*

*Mathematics Lounge, 6th Floor*

We hope you can join us as we celebrate the significant contributions of this year’s award winners and acknowledge the achievements of our graduating students.

Light refreshments will be served.

]]>Wednesday, May 17, 2017

11:10 a.m.

BA6183

PhD Candidate: Jonguk Yang

Supervisor: Michael Yampolsky

Thesis title: Applications of Renormalization in Irrationally Indifferent Complex Dynamics

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Abstract:

This thesis comprises of two main results which are proved using renormalization techniques.

For the first result, we show that a quadratic polynomial with a fixed Siegel disc of bounded type rotation number is conformally mateable with the basilica polynomial $f_B(z) := z^2-1$.

For the second result, we study sufficiently dissipative complex quadratic Hénon maps with a semi-Siegel fixed point of inverse golden-mean rotation number. It was recently shown by Gaidashev, Radu and Yampolsky that the Siegel disks of such maps are bounded by topological circles. We investigate the geometric properties of such curves, and demonstrate that they cannot be $C^1$-smooth.

A copy of the thesis can be found here: Jonguk Yang – Thesis Draft

]]>Wednesday, June 28, 2017

11:10 a.m.

BA6183

PhD Candidate: Kevin Luk

Co-Supervisors: Marco Gualtieri, Lisa Jeffrey

Thesis title:

******

Abstract:

A copy of the thesis can be found here:

]]>Friday, May 19, 2017

11:10 a.m.

BA6183

PhD Candidate: Tracey Balehowsky

Co-Supervisors: Spyros Alexakis, Adrian Nachman

Thesis title: Recovering a Riemannian Metric from Knowledge of the Areas of Properly-Embedded, Area-Minimizing Surfaces

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Abstract:

In this thesis, we prove that if $(M,g)$ is a $C^3$-smooth, 3-dimensional Riemannian manifold with mean convex boundary $\partial M$, which is additionally either a) $C^2$-close to Euclidean or b) $\epsilon_0$-thin, then knowledge of the least areas circumscribed by a simple closed curve $\gamma \subset \partial M$ and all perturbations $\gamma(t)\subset \partial M$ uniquely determines the metric. In the case where $(M,g)$ only has strictly mean convex boundary at a point $p\in\partial M$, we prove that knowledge of the least areas circumscribed by a simple closed curve $\gamma \subset U$ and all perturbations $\gamma(t)\subset U$ in a neighbourhood $U\subset \partial M$ of $p$ uniquely determines the metric near $p$.

A copy of the thesis can be found here: Balehowsky-PhD-thesis-draft-3May2017

]]>*Yuri Cher*

on Tuesday, March 28, 2017

at

10:30 a.m.

in

BA6183

40 St. George St.

~

Everyone is welcome to attend. Refreshments will be served in the Graduate Lounge.

Friday, March 24, 2017

4:10 p.m.

BA6183

PhD Candidate: Benjamin Schachter

Supervisor: Almut Burchard

Thesis title: An Eulerian Approach to Optimal Transport with Applications to the Otto Calculus

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Abstract:

This thesis studies the optimal transport problem with costs induced by Tonelli Lagrangians. The main result is an extension of the Otto calculus to higher order functionals, approached via the Eulerian formulation of the optimal transport problem. Open problems 15.11 and 15.12 from Villani’s Optimal Transport: Old and New are resolved. A new class of displacement convex functionals is discovered that includes, as a special case, the functionals considered by Carrillo-Slepčev. Improved and simplified proofs of the relationships between the various formulations of the optimal transport problem, first seen in Bernard-Buffoni and Fathi-Figalli, are given. Progress is made towards developing a rigourous Otto calculus via the DiPerna-Lions theory of renormalized solutions. As well, progress is made towards understanding general Lagrangian analogues of various Riemannian structures.

A copy of the thesis can be found here: DraftThesisSchachter

]]>A remembrance book will be available in the main office the week of March 20.

We look forward to having you join us.

]]>Tuesday, April 25, 2017

2:10 p.m.

BA6183

PhD Candidate: Yiannis Loizides

Supervisor: Eckhard Meinrenken

Thesis title: Norm-square localization for Hamiltonian LG-spaces

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Abstract:

In this thesis we prove norm-square localization formulas for two invariants of Hamiltonian loop group spaces: twisted Duistermaat-Heckman measures and a K-theoretic `quantization’. The terms in the formulas are indexed by the components of the critical set of the norm-square of the moment map. These results are analogous to results proved by Paradan in the case of Hamiltonian G-spaces. An important application of the norm-square localization formula is to prove that the multiplicity of the fundamental level k representation in the quantization is a quasi-polynomial function of k. This is closely related to the [Q,R]=0 theorem of Alekseev-Meinrenken-Woodward for Hamiltonian loop group spaces.

A copy of the thesis can be found here: YLThesis

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