Information for Current Students

Upcoming Courses - January to March 2019

One-off courses being run this term include:
Sobolev mappings into manifolds: nonlinear tools for the approximation, extension and lifting problems
Fridays 11am to 1pm (wks1-8) VC1

Mappings between Riemannian manifolds of Sobolev type regularity arise naturally in problems of calculus of variations and partial differential equations motivated by physical models and geometric problems. Because of their nonlinear character, Sobolev spaces of mappings between manifolds have notable differences with the classical linear Sobolev spaces. For instance, topological quantitative and qualitative obstructions arise recurrently and nonlinear constructions are required to prove their properties. Typical strategies involve avoiding singularities by suitable composition on the domain that effectively reduces the dimension, propagating values on higher dimensional sets and bringing back some values onto the target manifold by a suitable projection. This course will start from the approximation, extension and lifting problem for Sobolev maps, develop suitable nonlinear tools for their study and apply the latter to the solution of the problems. The approach will start from the perspective of mathematical analysis and will bring naturally some methods and concepts of homotopy theory for Riemannian manifolds.

Introduction to Rough Path Theory
Danyu Yang (Oxford)
9am to 11am Mondays (wks 1-8) C1

Rough path theory provides a fundamental explanation for various approximation methods to solving (stochastic) dynamic systems.  By identifying signature as the key object to introduce and to study a family of metrics on the space of paths. Rough path theory provides a robust solution to controlled differential equations driven by irregular signals which can be applied to Brownian motion, continuous semi-martingales, a large family of Gaussian processes and Markov processes.


PDE-CDT Hilary 2019 Schedule

Problem sheet hand in details

All graduate students, post-docs and faculty are welcome to come to the mini-courses. If you aren't a member of the CDT please just email to confirm you will be attending.

Student Seminars

Students give these talks to their peers to develop their skills.

Full details

Course Details

Details of the 4-year DPhil programme 


Course Handbooks

PDE CDT Handbooks

MI Handbook

MPLS Information for Graduate Students

Useful Links

Mathematics Taught Course Centre

MI Lecture Lists


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