Stanford University

Mon 11 Dec 2017, 3:00pm
Department Colloquium
MATX 1100

Cobordism categories and moduli spaces of manifolds

MATX 1100
Mon 11 Dec 2017, 3:00pm4:00pm
Abstract
Let M be a smooth manifold, let Diff(M) denote the topological group of seldiffeomorphisms, and let BDiff(M) denote the "classifying space”. For any paracompact space X, there is a oneone correspondence between the set of homotopy classes [X, BDiff(M)] and the set of isomorphism classes of fibre bundles over X with fibre M. The classifying space BDiff(M) is referred to as the "moduli space of manifolds of type M". The study of the homotopy type of these spaces occupies a central place in smooth topology.
In this talk I will discuss some contemporary approaches to studying the homotopy/homology of BDiff(M), for varying M. In particular I will discuss the results of Madsen and Weiss on the stable moduli spaces of Riemann surfaces and the results of Galatius and RandalWilliams on the stable moduli spaces of manifolds of dimension 2n. I will then present recent work of mine pertaining to the moduli spaces of odd dimensional manifolds, and manifolds with boundary, and discuss connections to cobordism categories and surgery theory.
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Université de Sherbrooke

Wed 13 Dec 2017, 3:00pm
Department Colloquium
MATX 1100

A snapshot of Heegaard Floer theory

MATX 1100
Wed 13 Dec 2017, 3:00pm4:00pm
Abstract
Heegaard Floer homology provides a suite of invariants for studying threemanifolds, introduced by Ozsváth and Szabó. This theory has, more recently, been expanded to treat manifolds with boundary through bordered Floer homology, providing the tools required to answer natural questions that arise when decomposing a threemanifold along a surface. This talk aims to provide a brief overview of Heegaard Floer theory, give a sense for some of the questions driving its study, and point to some recent progress on answering these.
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Seminar Information Pages

Note for Attendees
Refreshments will be served in MATX 1100 at 2:30p.m. before this Mathematics Colloquium.