In the video below, I explain how to derive Kaluza Klein action which occurs from generalizing the Einstein-Hilbert action to five dimensions. The grand implication of this is that gravity and electromagnetism are unified!
Our new article was recently published in The Journal of Geometry and Physics. It is shown that under certain conditions, The Einstein Field Equations have the same form as a fold bifurcation seen in Dynamical Systems theory, showing even a deeper connection between General Relativity and Dynamical Systems theory! (You can click the image below […]
Here is a link to my lectures on nonlinear dynamical systems given at York University during the Winter semester of 2017. These lectures start off with manifold theory, and end with examples in biology, game theory, and general relativity/cosmology.
Our new paper examining the dynamics of an asymmetric Hawk-Dove game was published in The International Journal of Differential Equations:
In the final two lectures of my differential equations class , I discussed how Dynamical Systems theory can be used to understand and describe the dynamics of cosmological solutions to Einstein’s field equations. Videos and lecture notes posted below: Lecture Notes:
It was pointed out to me recently that a few of the articles I have written describing the detailed geometric structure behind the triangle offense is scattered in various places around my blog, so here is a list of the articles in one convenient place: The Mathematics of Filling the Triangle (First article) Group Theory and […]
In a previous post, I showed how given random positions of 5 players on the court that they could “fill” the triangle. The main geometric constraint is that 5 players can form 3 triangles on the court, and that due to spacing requirements, these triangles are “optimal” if they are equilateral triangles. Given that we […]
Most people when talking about cosmology typically talk about the universe in one context, that is, as a particular solution to the Einstein field equations. Part of my research in mathematical cosmology is to try to determine whether the present-day universe which we observe to be very close to spatially flat and homogeneous, and very […]