The Academy for the Mathematical Sciences has announced its first cohort of fellows, 100 in total from across academia and teaching, science communication and business. Twelve of those fellows are from Oxford, spread across four departments, reflecting the reach and importance of mathematics.
17:00
Rhythmicity and Coordination: The Importance of Circadian and Seasonal Biology - Russell Foster
Biology is not constant but highly rhythmic. This includes the fast rhythms of action potentials in the nervous system and the pulsatile release of hormones. At a longer time-scale are the daily (circadian) rhythms and annual rhythms observed across much of the biological world. This talk will consider the mechanisms and importance of circadian rhythms to human health and the role of seasonal timing in reproduction and other phenomena in birds, mammals and humans. In biology, like the rest of science, timing is everything.
Russell Foster is Professor of Circadian Neuroscience and the Head of the Nuffield Laboratory of Ophthalmology in Oxford. He has featured widely in print and broadcast media on the subject of sleep and circadian rhythms and is the author of several popular books on the subject.
Please email external-relations@ maths.ox.ac.uk to register to attend in person.
The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Thursday 5 March at 5-6 pm and any time after (no need to register for the online version).
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
Independent set count and independent transversal connectedness
Abstract
I discuss two separate projects which evoke/strengthen connections between combinatorics and ideas from statistical physics.
The first concerns the minimum number of independent sets in triangle-free graphs of a given edge-density. We present a lower bound using a generalisation of the inductive method of Shearer (1983) for the sharpest-to-date off-diagonal Ramsey upper bound. This result is matched remarkably closely by the count in binomial random graphs.
The second sets out a qualitative generalisation of a well-known sharp result of Haxell (2001) for independent transversals in vertex-partitioned graphs of given maximum degree. That is, we consider the space of independent transversals under one-vertex modifications. We show it is connected if the parts are strictly larger than twice the maximum degree, and if the requirement is only at least twice the maximum degree we find an interesting sufficient condition for connectivity.
These constitute joint works with Pjotr Buys, Jan van den Heuvel, and Kenta Ozeki.
If time permits, I sketch some thoughts about a systematic pursuit of more connections of this flavour.