Colloquium - Postdoc Threads
Title: Postdoc Threads
Speakers: Taboka Chalebgwa (McMaster), Sabrina Streipert (McMaster) and Jeremy Lane (McMaster)
Geometry of complex polynomials, rational points on transcendental curves and other things... - Taboka Chalebgwa
I will give a brief survey of some of the themes appearing in our recent work. We will begin with a quick discussion of a result in the geometry of complex polynomials and then move on to some results related to the seminal works of Bombieri-Pila-Wilkie. Time permitting, I will also give a soupçon of some of our current projects.
Non-standard discretization of a delay population model - Sabrina Streipert
The presentation addresses a recent work that formulates a discretization of a delay population model in a non-standard fashion. Rather than applying a discretization scheme to a continuous model, as commonly done, we derive the model from first principles. The delay population model we discretise is an alternative model to the so-called classical Hutchinson model. While the Hutchinson model considers a delay in the net-per capita growth rate, the alternative version we consider here assumes a delay only in the growth contribution that takes into account that those individuals that die during the delay, do not contribute to growth. The analysis of our delay difference equation model identifies a critical delay threshold. If the time delay exceeds this threshold, the model predicts that the population will go extinct for all non-negative initial conditions and if it is below this threshold, the population survives, and its size converges to a positive globally asymptotically stable equilibrium that is decreasing in size as the delay increases.
Integrable systems and symplectic geometry - Jeremy Lane
Abstract: An integrable system is a physical system with many symmetries. The study of integrable systems is one largely driven by examples. New examples of integrable systems are rare and, when they are discovered, tend to be very useful.
My research gives new general constructions of large families of examples of integrable systems on symplectic manifolds. In this talk I will give a brief introduction to integrable systems on symplectic manifolds and my research.
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