13:00
Dowker duality: new proofs and generalizations
Abstract
I will present short, new proofs of Dowker duality using various poset fiber lemmas. I will introduce modifications of joins and products of simplicial complexes called relational join and relational product complexes. Using the relational product complex, I will then discuss generalizations of Dowker duality to settings of relations among three (or more) sets.
13:00
Intrinsic bottleneck distance in merge tree space
Abstract
Merge trees are a topological descriptor of a filtered space that enriches the degree zero barcode with its merge structure. The space of merge trees comes equipped with an interleaving distance dI , which prompts a naive question: is the interleaving distance between two merge trees equal to the bottleneck distance between their corresponding barcodes? As the map from merge trees to barcodes is not injective, the answer as posed is no, but as proposed by Gasparovic et al., we explore intrinsic metrics dI and dB realized by infinitesimal path length in merge tree space, which do indeed coincide. This result suggests that in some special cases the bottleneck distance (which can be computed quickly) can be substituted for the interleaving distance (in general, NP-hard).
Despite being Week 5 of term, it's never too late to get involved in student-led societies! The Invariants still have lots of events coming up this side of Christmas, including a talk by Giulia Celora on The Mathematics of Biological Self-Organisation, a hot chocolate social, and their Integration Bee!
More details on all events can be found on their website: https://www.invariants.org.uk/events
A clip from Robin Wilson's series on the equations that made mathematics. You can have a peep at all the talks so far.
The EPSRC Doctoral Studentships in Mathematics and Statistics Innovation at Heriot Watt University are now open for applications.
EPSRC Doctoral PhD studentships roles are funded by the Engineering and Physical Sciences Research Council (EPSRC) as part of Heriot-Watt University’s Doctoral Training Partnership award.