Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.
BA6183

PhD Candidate:  Jonguk Yang
Co-Supervisors:  Michael Yampolsky
Thesis title:

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Abstract:

 

A copy of the thesis can be found here:

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.
BA6183

PhD Candidate:  Kevin Luk
Co-Supervisors:  Marco Gualtieri, Lisa Jeffrey
Thesis title:

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Abstract:

 

A copy of the thesis can be found here:

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

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:

 

A copy of the thesis can be found here: Tracey_Balehowsky_thesis_PhD_April19_2017

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

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