Algebraic Topology of Manifolds

Monday, September 11, 2017 to Friday, September 15, 2017

LMS-CMI Research School

Andrew Wiles Building
University of Oxford

Organizer: Ulrike Tillmann (Oxford)

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Overview

Manifolds are at the centre of much of geometry and topology, and through the influence of axiomatic topological quantum field theory they have become an important organizing force in category and representation theory.

Classically, in the 1960s, algebraic topology was at the heart of their classification theory in form of characteristic classes and characteristic numbers, cobordism theory, surgery theory, and later Waldhausen's K-theory of manifolds. By the 1980s the machinery got heavy with diminishing returns. We are now experiencing a renaissance of the field as well as a paradigm shift where manifolds not only are the objects of study but become the tools.

The school aims at inspiring the next generation with this exciting success story of interwoven ideas bouncing between different fields, and giving the participants the tools to contribute to this lively research area.

Additional Information

Programme

There will be four lecture series with exercises and tutorials. In addition there will be guest lectures and a forum in which participants will be able to briefly introduce their own research topics.

Dan Freed: Topological Quantum Field Theory
Oscar Randal-Williams: Characteristic classes and moduli spaces of manifolds
Greg Arone: The Goodwillie-Weiss embedding calculus
Nathalie Wahl: Homology stability

A schedule will be available here.

The academic programme will be complimented by a social programme of ghost tours, punting, pub dinner and games in the University Parks.

Registration

On-line registration is now open here. Referees should use the on-line form here.

Funding

Research students who will not have completed their PhD’s by the start of the Research School and who would otherwise be unable to attend can apply for financial aid.

Location

The research school will take place in the Andrew Wiles Building at theMathematical Institute in Oxford, OX2 6GG.

Accommodation

Accommodation has been arranged in Somerville College, OX2 6HD, which is right next to the Mathematical Institute. This can be booked through the on-line registration system. Check-in is from 2pm onwards, and check-out is at 10am. There will be a porter on duty all the time.

For alternative university accommodation in Oxford please see here. For other accommodation please see here.

Travel information

Heathrow is the most convenient airport, with regular buses direct to Oxford.

More detailed travel information can be found at the departmental website: Directions to the Mathematical Institute

This workshop is principally funded by the Clay Mathematical Institute. Additional support has been received from the London Mathematical Society and the Heilbronn Institute. We also thank the Mathematical Institute, Oxford University, for providing lecture and class rooms.

Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

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