My name Belgin Seymenoğlu. I am a maths PhD student at UCL, which is also where I gained my MSci in Mathematics with Mathematical Physics. Welcome to my academic webpage!
Many models in population genetics feature some form of convergence of the genetic state of the population, typically onto a so-called invariant manifold. This allows one to effectively reduce the the dynamical system to a problem with fewer dimensions, making it easier to investigate the stability of the fixed points in the model, as well as to predict the long-term evolution of the population.
In some models, an invariant manifold is known to exist, but with some very restrictive assumptions such as weak selection. My aim is to prove the existence of an invariant manifold for a handful of models in population genetics without relying on such assumptions, hence my results will be much more widely applicable.
I investigated Cosserat models of elasticity for my MSci project. Unlike classical elastic models, which neglect the local structure of points in an elastic body, Cosserat models take into account both the change in position of points and the so-called microstructure, in which said points are allowed to undergo rigid rotations. In my project, I analysed coupled elastic and rotational waves in the Cosserat model of Continuum mechanics and found some interacting soliton solutions. Moreover, I created the colourful animation below using Mathematica to visualise these waves. I have since written a paper about my project (see my list of publications).
Since then, I have started comparing my Cosserat model with Skyrme's model from particle physics. The first step will be to put together a translation from Skyrme to Cosserat!
My office is in Room M201 of the Kathleen Lonsdale Building. Instructions for finding this room are given here.
I am teaching the undergraduate course Mathematics for Engineers 1 (MATH6501). All the lecture material for this course can be found on Moodle. However, if you cannot log into Moodle, you can download the material from here instead:
This term I have the following tutor groups:
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