Since June 2016, he has been employed as a University Lecturer at Leiden University Centre for Linguistics, Leiden University, after having worked at different institutions in Denmark, Mexico, Germany and Russia, including, during 2003-2015, the Department of Linguistics, Max Planck Institute for Evolutionary Anthropology.
Wichmann's PhD dissertation, from the University of Copenhagen, treated the Azoyú variety of Tlapanec spoken in Guerrero, Mexico.
Regarding Mixe–Zoquean, he has done comparative work resulting in the currently most accepted classification of the Mixe–Zoquean language family as well as a reconstruction of its vocabulary and grammar (Wichmann 1995).
He also specializes in the study of Maya hieroglyphs — particularly the linguistic aspects of the deciphering of the Mayan script.
Since its inception in 2011, Wichmann has been General Editor of Language Dynamics and Change.