I am an associate professor at the Department of Geometry within the Institute of Mathematics of the Budapest University of Technology and Economics. Previously, I was a postdoctoral researcher at ETH Zurich and at the Technical University of Munich. I recieved my PhD from the Doctoral School of Physics, Budapest University of Technology and Economics.
In 2019 I was awarded a János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
My main research interest is in mathematical aspects of quantum information theory, especially asymptotic transformations in entanglement theory and other resource theories. In my work I use tools from various areas of mathematics, including representation theory, information theory, and matrix analysis.
Most important publications

Matthias Christandl, Péter Vrana, and Jeroen Zuiddam, Universal points in the asymptotic spectrum of tensors
Journal of the American Mathematical Society, 2021
arXiv, doi 
Matthias Christandl, Péter Vrana, and Jeroen Zuiddam, Barriers for fast matrix multiplication from irreversibility
Theory of Computing, 17(2):1–32, 2021
arXiv, doi 
Péter Vrana and Matthias Christandl, Entanglement distillation from Greenberger–Horne–Zeilinger shares
Communications in Mathematical Physics, 352(2):621–627, 2017
arXiv, doi 
Asger Kjærulff Jensen and Péter Vrana, The asymptotic spectrum of LOCC transformations
IEEE Transactions on Information Theory, 66(1):155–166, 2019
arXiv, doi 
Alonso Botero, Matthias Christandl, and Péter Vrana, Large deviation principle for moment map estimation
Electronic Journal of Probability, 26:1–23, 2021
arXiv, doi 
Péter Vrana and Matthias Christandl, Distillation of Greenberger–Horne–Zeilinger states by combinatorial methods
IEEE Transactions on Information Theory, 65(9):5945–5958, 2019
arXiv, doi 
Péter Vrana, Asymptotic continuity of additive entanglement measures
IEEE Transactions on Information Theory, 68(5):3208–3217, 2022
arXiv, doi 
Péter Vrana, Probabilistic refinement of the asymptotic spectrum of graphs
Combinatorica, 41:873–904, 2021
arXiv, doi 
Christopher Perry, Péter Vrana, and Albert H Werner, The semiring of dichotomies and asymptotic relative submajorization
IEEE Transactions on Information Theory, 68(1):311–321, 2022
arXiv, doi