Welcome to my homepage, which is still very much a work in progress. My aim is to make some of my unpublished work on mathematics and game theory available here and, perhaps, add some links to music sites I like and some pictures from concerts I attended. Besides getting these pages cleared up, my current aim is to upload my first and last academic work.

By the way, the way, this is not me in the picture. It is Clark Kent imposed on a picture of me on Dartmoor. Even the glasses are not mine. That's what chatGPT understands when I ask it to draw a picture of me in the style of a Superman comics from the 60's... I will keep it here until a more realistic and less flattering version is available.

Game Theory

The latest work on game theory by my co-author Dries Vermeulen should also find its way here soon. It is about the notion of a regular equilibrium points as defined by Harsany. As an implication of the implicit function theorem Harsanyi shows that if an equilibrium point is regular then the Nash equilibrium correspondance is nearby locally a smooth function with a smooth inverse. We show that the inverse also holds. This is surprising because in analysis point conditions on the derivatives of a function typically only give necessary, not sufficient conditions on the local behaviour of a function. There must be more going on.

Music Fan

Every month there is a real treat just a few hundred meters from where I live: The Blue Vanguard Jazz Club is at the Cygnet Theatre. The brilliant Jazz trio consisting of Craig Milverton (p), Al Swainger (b) and Coach York (dr) accompany a guest musician. Over the years I have seen an amazing range of outstanding musicians, mostly from the British Jazz scene. Here are some pictures I took at these gigs.

Mathematics

My first academic work is my diploma thesis in mathematics, co-written with Franz-Josef Bilitewski and Richard Bauer. A complete scan of the thesis on singularity theory, written in German on (probably) the first Olivetti electronic typewriters, can be downloaded from these pages. I have used AI to create, as a latex file in English, the table of contents and the introduction to the thesis with a table listing all the deformations that we have calculated. Hopefully I will be able over time to create a complete latex version of the thesis, but it seems to be a VERY slow process with each chapter taking a couple of days.

Thanx

A big, big thank you to my former student Suliman Saleh. Due to him I have the rights on the name "balkenborg.com". Using AI he created a complete website to help me. It gives a highly idealized version of me as a researcher and teacher, including purely fictitious papers and projects. It was inspiring and helpful and superior to the pages I offer here.

Thanks to my brother-in-law Myron Stephenson. He helped me with a lot of technical aspects like getting a site, transfering the domain name and setting up Joomla for me. I should have been less ambitious. Joomla is not well documented and I made not much progress on these new pages before I started to get the help of chatGPT. (I actually was one of the first economists to create a homepage. I did it when I was still in Southampton, in 1998 or slighlty earlier. It was written in very simple HTML and I only minimally updated it with new materials until the university closed down all personal homepages for security reasons...)  

Thanks to the musician Al Swainger for reporting on his use of AI in his weekly letters to subscribers. It was encouraging. Finally, thanks to the Belgian comedian and science communicator Lieven Scheire for his brilliant talk on AI. That got me going and now I ask AI for anything technical to create this site.