Manifolds

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Workshop theme

The relationship between the topology of manifolds and homotopy theory has been recently strengthened in several ways, harking back to the close connection which existed between these subjects in their early development.

One direction has been the circle of ideas arising from Madsen--Weiss' proof of Mumford's conjecture, with cobordism theory attracting new interest in the modern guise of cobordism categories, and applications to the study of automorphism groups of manifolds by a method quite different to the classical route, via surgery theory, pseudoisotopy theory, and Waldhausen's algebraic K-theory of spaces. Another direction, related to the previous one, is Lurie's development of a close connection between extended Topological Quantum Field Theories and ideas from the homotopy theory of higher categories, where the theory of manifolds may be encoded as a universal object in higher category theory. A third direction, again related to the previous one, is the notion of factorisation homology. This is a pairing between n-manifolds and n-categories: regarded as an invariant of manifolds, it is a promising source of sensitive manifold and linking invariants; regarded as an invariant of higher categories, it codifies their infinitesimal structure.

This workshop will bring together mathematicians working at the forefront of these and related areas, to develop new foundational results, pursue applications, and relate these new ideas with more classical work in the topology of manifolds.

Timetable

Monday 3rd December 2018
09:00 to 09:50	Registration	No Room Required
09:50 to 10:00	Welcome from Christie Marr (INI Deputy Director)	Room 1
10:00 to 11:00	Soren Galatius University of Copenhagen H_{4g-6}(M_g)	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Alexander Kupers Harvard University Cellular techniques in homological stability 1: general theory	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
14:30 to 15:30	George Raptis Universität Regensburg The h-cobordism category and A-theory	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Christopher Schommer-Pries University of Notre Dame The Relative Tangle Hypothesis	Room 1
17:00 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 4th December 2018
09:00 to 10:00	Wolfgang Lueck On the stable Cannon Conjecture	Room 1
10:00 to 11:00	Thomas Willwacher ETH Zürich Configuration spaces of points and real Goodwillie-Weiss calculus	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Alexander Kupers Harvard University Cellular techniques in homological stability 2: mapping class groups	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
14:30 to 15:30	Victor Turchin Kansas State University Embeddings, operads, graph-complexes	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Nathalie Wahl University of Copenhagen Homotopy invariance in string topology	Room 1

Wednesday 5th December 2018
09:00 to 10:00	Cary Malkiewich Binghamton University Periodic points and topological restriction homology	Room 1
10:00 to 11:00	Christine Vespa University of Strasbourg Higher Hochschild homology as a functor	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Fabian Hebestreit University of Bonn The homotopy type of algebraic cobordism categories	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 18:00	Free afternoon	No Room Required

Thursday 6th December 2018
09:00 to 10:00	Alexander Berglund Stockholm University Rational homotopy theory of automorphisms of manifolds	Room 1
10:00 to 11:00	Johannes Ebert Westfalische Wilhelms-Universitat Munster Cobordism categories, elliptic operators and positive scalar curvature	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Ben Knudsen Harvard University Configuration spaces and Lie algebras away from characteristic zero	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
14:30 to 15:00	Manuel Krannich University of Cambridge Contributed talk - Mapping class groups of highly connected manifolds	Room 1
15:00 to 15:30	Rachael Boyd Norwegian University of Science and Technology Contributed Talk - The low dimensional homology of Coxeter groups	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Csaba Nagy University of Melbourne Contributed Talk - The Sullivan-conjecture in complex dimension 4	Room 1
16:30 to 17:00	Danica Kosanović Max-Planck-Institut für Mathematik, Bonn Contributed talk - Extended evaluation maps from knots to the embedding tower	Room 1
18:15 to 19:15	Reception at Cambridge University Press Bookshop	No Room Required
19:30 to 20:30	Formal Dinner at Christs College (Hall 110)	No Room Required

Friday 7th December 2018
10:00 to 11:00	Andre Henriques University of Oxford The complex cobordism 2-category and its central extensions	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Sam Nariman Northwestern University Topological and dynamical obstructions to extending group actions.	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:30	Ryan Budney Some prospects with the splicing operad	Room 1
14:30 to 15:30	Diarmuid Crowley University of Melbourne Relative kappa-classes	Room 1