The Takagi function and its generalizations

Abstract: The Takagi function is a classical example of a continuous nowhere differentiable function which continues to inspire, fascinate and puzzle mathematicians on account of its interesting properties. It has appeared in a surprising number of different mathematical contexts such as mathematical analysis, probability theory and number theory. This talk is made of two clearly differentiated parts. The first part of the talk will be devoted to presenting some of these properties in order to gain more insight into the role of the Takagi function within the contexts mentioned above. Throughout the years, several generalizations of the Takagi function have come to light in an effort to extend such properties to a wider family of functions. In the second part of the talk we will show the two most studied generalizations, namely Takagi-Van der Waerden functions and the Takagi class.