Since April 2021 I work at Karlsruher Institute für Technologie in the Topology group led by Roman Sauer.
I was an assistant professor at the Adam Mickiewicz University between 2014 and 2021. The Mathematical Institute of the Polish Academy of Sciences hosted me as visiting professor between 2015 and 2017, where I worked with Piotr Nowak on Kazhdan’s property (T). Between 2019 and 2021 I was a postdoc in the MATH+ programm hosted at Technische Universität Berlin in the group of Michael Joswig, where I was working on machine learning aspects of polytope theory.
My research interests also include: geometric group theory (therefore: group actions), optimisation as well as symbolic and certified computation. Before, I used to work on topology of high-dimensional manifolds (surgery and equivariant surgery theory) and applied topology (persistence and others). An important part of my research has become programming – the effects may be found on github or here.
Programming languages: Julia, Python Sport: Climbing, Yoga
PhD in Mathematics, 2014
Adam Mickiewicz University
MSc in Mathematics, 2010
Adam Mickiewicz University
We prove that $\operatorname{Aut}(F_n)$ has Kazhdan’s property (T) for every $n \geqslant 6$. Together with the previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \geqslant 5$. We also provide new, explicit lower bounds for the Kazhdan constants of $\operatorname{SAut}(F_n)$ (with $n \geqslant 6$) and of $\operatorname{SL}_n(\mathbb{Z})$ (with $n \geqslant 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n > 6$.
We prove that $\operatorname{Aut}(\mathbb{F}_5)$ has Kazhdan’s property (T).