Poets and academics have defined mathematics as the language of nature or the most coherent codification of reality. Dirk Erhard’s project seems to follow this principle, which seeks universal patterns in probabilistic and complex physics processes whose results cannot be expressed by a normal distribution.
Born in Germany, Erhard was a five-time national medalist in trampoline jumping as a child. He devoted nine years to the sport before fully focusing on mathematics. He earned his bachelor’s and master’s degrees from Technische Universität Berlin and his doctorate in natural sciences and mathematics from Leiden University in the Netherlands.
Dirk Erhard met and married a Brazilian doctoral student in biology in Leiden. He left Europe for Brazil to be with his wife and is now an adjunct professor at the Federal University of Bahia. The couple learned the traditional German bread recipe to preserve the mathematician’s family tradition. Erhard also enjoys swimming and running to oxygenate and de-stress from work.
Imagine tossing a coin in a game of heads or tails many times. We expect that the coin will come up heads roughly 50% of the time. However, because the outcome of each toss is random, there will be some fluctuation around this 50%. One of the main results of probability theory is that this fluctuation follows the normal distribution. The same logic applies to other random experiments, such as rolling a die. This suggests that the normal distribution is a universal object independent of the specific details of the random experiment.
In this project, we will investigate the universality of more complex random processes often used to model phenomena in physics. We will focus on three different types of systems: processes with geometric constraints that induce global correlations in time, processes interacting with a random environment, and singular stochastic differential equations.