15:45
Trying to understand mapping class groups of algebraic surfaces from the Thurstonian point of view
Abstract
In some ways the theory of mapping class groups of 4-manifolds is in 2020 at the same place where the theory of mapping class groups of 2-manifolds was in 1973, before Thurston changed everything. In this talk I will describe some first steps in an ongoing joint project with Eduard Looijenga where we are trying to understand mapping class groups of certain algebraic surfaces (e.g. rational elliptic surfaces, and also K3 surfaces) from the Thurstonian point of view.
North Meets South
Abstract
Paolo Aceto
Knot concordance and homology cobordisms of 3-manifolds
We introduce the notion of knot concordance for knots in the 3-sphere and discuss some key problems regarding the smooth concordance group. After defining homology cobordisms of 3-manifolds we introduce the integral and rational homology cobordism groups and briefly discuss their relationship with the concordance group. We conclude stating a few recent results and open questions on the structure of these groups.
North Meets South
Abstract
The classical Riemann-Hilbert correspondence is an elegant statement linking geometry (via flat connections) and topology (via local systems). However, when one allows the connections to have even simple singularities, the naive correspondence breaks down. We will outline some work on understanding this "logarithmic" setting.
Guidance in applying for EPSRC fellowships
Abstract
In this session, Laura will explain the process of applying for an EPSRC fellowship. In particular, there will be a discussion on the Future Leaders Fellowships, New Investigator Awards and Standard Grant applications. There will also be a discussion on applying for EPSRC funding more generally. Laura will answer any questions that people have.
Oxford Mathematicians Dmitry Belyaev and Michael McAuley explain the ubiquitous role of Gaussian Fields in modelling spatial phenomena across science, and especially in cosmology. This case-study is based on work with Stephen Muirhead at Queen Mary University of London (QMUL).
OCIAM learns ... about exponential asymptotics
A new bi-weekly seminar series, 'OCIAM learns...."
Internal speakers give a general introduction to a topic on which they are experts.
Inverting a signature of a path
Abstract
Abstract: The signature of a path is a sequence of iterated coordinate integrals along the path. We aim at reconstructing a path from its signature. In the special case of lattice paths, one can obtain exact recovery based on a simple algebraic observation. For general continuously differentiable curves, we develop an explicit procedure that allows to reconstruct the path via piecewise linear approximations. The errors in the approximation can be quantified in terms of the level of signature used and modulus of continuity of the derivative of the path. The main idea is philosophically close to that for the lattice paths, and this procedure could be viewed as a significant generalisation. A key ingredient is the use of a symmetrisation procedure that separates the behaviour of the path at small and large scales.We will also discuss possible simplifications and improvements that may be potentially significant. Based on joint works with Terry Lyons, and also with Jiawei Chang, Nick Duffield and Hao Ni.