"God used beautiful mathematics in creating the world." Paul Dirac
Research
My research interests
As a PhD student I started working in the Local Theory of Banach Spaces, which is the part of Functional Analysis that studies the geometry of finite-dimensional subspaces - the so-called local structure - of Banach spaces to gain information on the geometry of the space itself, that is, its global structure. Of special interest to me is the local structure of the classical Banach spaces Lp, in particular the finite-dimensional subspaces with a symmetric or unconditional basis. Despite using functional analytic tools, combinatorial and probabilistic methods are an integral part.
The Local Theory of Banach Spaces is naturally connected to Asymptotic Convex Geometry, which studies the geometry of convex bodies as the dimension tends to infinity.
Here I am interested in the geometry of random polytopes inside isotropic convex bodies. Again, despite geometric ideas, probabilistic tools are important to understand the structure of random convex sets. Both areas are a part of what is nowadays known as Asymptotic Geometric Analysis. Recently I started working in Random Matrix Theory with particular interest in the singular values of random matrices with independent entries that are not necessarily identically distributed. I am also interested in applications of Asymptotic Geometric Analysis to, e.g., Compressed Sensing or problems in Information-Based Complexity, in particular high-dimensional numerical integration.