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| 2002 - 2006 | PhD, Indiana University, Bloomington, IN, USA | | 2006 - 2008 | Postdoctoral Fellow, University of British Columbia, Vancouver, BC, Canada | | 2008 - 2011 | Professor (W2, Bonn Junior Fellow), University of Bonn | | Assistant Professor, University of Szeged, Hungary |
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One of my interests has been the interplay of probabilistic models and geometric group theory. I have been working on the questions of how critical probabilities (for the existence of one, or of infinitely many infinite clusters) and critical exponents behave for Cayley graphs of various properties (in particular, what is preserved by quasi-isometries). In [1], we introduce a new coarse-geometric invariant, the separation profile of groups, giving rise to several questions (e.g., what separation functions may arise for a Cayley graph?) that I would like to investigate further. Another focus of my interests is stochastic optimization problems in an infinite setup. We have recently found an allocation rule of optimal tail for the Poisson point process, but work is still in progress on whether it can be applied to give optimal matching rules, and whether the allocation rule can be generated in some “canonical” way (as in case of gravitational allocation).
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- Diplom theses: 2, currently 2
- PhD theses: 1, currently 1
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