University of Glasgow

Quiver varieties, as introduced by Nakaijma, play a key role in representation theory. They give a very large class of symplectic singularities and, in many cases, their symplectic resolutions too. However, there seems to be no general criterion in the literature for when a quiver variety admits a symplectic resolution. In this talk I will give necessary and sufficient conditions for a quiver variety to admit a symplectic resolution.  This result is based on work of Crawley-Bouvey and of Kaledin, Lehn and Sorger. The talk is based on joint work with T. Schedler.
 

The timing of developmental milestones such as egg hatch or bud break

can be important predictors of population success and survival. Many

insect species rely directly on temperature as a cue for their

developmental timing. With environments constantly under presure to

change, developmental timing has become highly adaptive in order to

maintain seasonal synchrony. However, climatic change is threatening

this synchrony.

Our model couples existing models of developmental timing to a

quatitative genetics framework which descibes the evolution of

developmental parameters. We use this approach to examine the ability of a

population to adapt to an enviroment that it is highly maladapted to.

Through a combination of numerical and analtyical approaches we explore

the dynamics of the infinite dimensional system of

integrodifference equations. The model indicates that developmental timing

is surprisingly robust in its ability to maitain synchrony even under

climatic change which works constantly to maintain maladaptivity.