Welcome to my website

My name is 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!

Research

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.

The Nagylaki-Crow model
The Nagylaki-Crow model mapped to an open quadrant
The Nagylaki-Crow model focuses on one locus with two alleles and involves differential fertilities and death rates for each genotype. In some cases the invariant manifold (magenta) may be nonconvex (left) or it can fail to be unique (right).
Selection-Recombination manifold
Selection-Recombination manifold
I also studied a two-locus-two-allele model focusing on the genetic processes of selection and recombination. The invariant manifold for this system (green) represents a balance between these two processes. I am currently writing a paper about this project!

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).

My soliton solutions in action. Each ring can be thought of as a point in an elastic body. Rotations of the rings represent microrotations, while displacements of the rings correspond to classical elastic waves.

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!

Publications

2018

2016

Teaching

My office is in Room M201 of the Kathleen Lonsdale Building. Instructions for finding this room are given here.

I taught the following first-year tutor groups:

2016-2017

  • MATH1301 others

2015-2016

  • Mathematics with Economics
  • Mathematics and Statistics

2014-2015

  • Mathematics
  • Mathematics and Statistics

Awards

2018

2017

Popular articles

I am a member of the team behind Chalkdust, a UK maths magazine for the mathematically curious.

This April the KLB had a re-opening ceremony, during which we demonstrated a pile of matchboxes that can learn how to play noughts and Crosses to David Attenborough and others. We even got him to take away three issues of our magazine!

Chalkdust articles:

Issue 07

Chalkdust blog posts: