During the pandemic, Judy Kennedy and I, later joined by Goran Erceg, began investigating the dynamics of closed relations in dynamical systems, which we termed CR-dynamical systems. With travel restrictions in place, we established regular online meetings to collaborate on this research. Our initial focus was on fixed-point problems from the perspective of closed relations, which led us to explore broader dynamical properties and ultimately to introduce Mahavier dynamical systems.

Despite being spread across different time zones–Judy in the US, Goran in Croatia, and I in Slovenia–we managed to coordinate meetings in the early evening for Goran and me, and at 1:30 PM for Judy. Since then, we have published numerous papers on Mahavier dynamical systems, with several more in progress. Once travel resumed, Goran and I visited Judy in the US twice, while Judy visited Slovenia and Croatia on many more ocations, allowing us to collaborate in person. While online meetings and screen-sharing have been invaluable, we recognize that nothing fully replaces in-person discussions.

Our research has continued to gain momentum, and we are committed to furthering this long-term project. We believe our work is both fundamental and significant, and we remain excited about its potential. Along the way, we named our group the Topology Nerds, and later, Van Nall, Sina Greenwood, Rene Gril Rogina, Chris Mouron and Ivan Jeli' c joined our efforts.

In this talk, I will present an overview of the most important results achieved by the Topology Nerds group.