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.
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).
14:15
Quantum K-theory and 3d A-model
Abstract
I will discuss some ongoing work on three-dimensional supersymmetric gauge theories and their relationship to (equivariant) quantum K-theory. I will emphasise the interplay between the physical and mathematical motivations and approaches, and attempt to build a dictionary between the two. As an interesting example, I will discuss the quantum K-theory of flag manifolds. The QK ring will be related to the vacuum structure of a gauge theory with Chern-Simons interactions, and the (genus-0) K-theoretic invariants will be computed in terms of explicit residue formulas that can be derived from the relevant supersymmetric path integrals.
Nebulae
LIGO-Virgo's First Gravitational-Wave Transient Catalog