Mailing address

Alfréd Rényi Institute of Mathematics
H-1053 Budapest, Reáltanoda u. 13-15.
E-mail: titkos@renyi.hu
Office: III/16

Research interests 

Functional analysis, Optimal transport and Wasserstein spaces, Lipschitz-free spaces

Awards, Scolarships

- Alexits Prize of the Hungarian Academy of Sciences (2021)

János Bolyai Research Fellowship (2018)

- Bolyai+ Scholarship - New National Excellence Programme (2018,2019,2020)

- Youth Award of the Hungarian Academy of Sciences (2018)

- NRDI Postdoctoral Fellowship (2018)

Editorial work

2019- Editor of Periodica Mathematica Hungarica

2020- Editor of Érintő (Electronic Journal of the János Bolyai Mathematical Society)

Selected Papers
1. On the exotic isometry flow of the quadratic Wasserstein space over the real line
Linear Algebra and its Applications, 2024
DOI: https://doi.org/10.1016/j.laa.2023.02.016 (with Gy.P. Gehér, and D. Virosztek)

2.Quantum Wasserstein isometries on the qubit state space
Journal of Mathematical Analysis and Applications, 2023

3. Isometric rigidity of Wasserstein tori and spheres
Mathematika, 2023
DOI: https://doi.org/10.1112/mtk.12174
(with Gy.P. Gehér, and D. Virosztek)

4. Isometric rigidity of Wasserstein spaces: the graph metric case

Proceedings of the American Mathematical Society, 2022
DOI: https://doi.org/10.1090/proc/15977  (with G. Kiss)

5. The isometry group of Wasserstein spaces: the Hilbertian case
Journal of the London Mathematical Society, 2022
DOI: https://doi.org/10.1112/jlms.12676 
(with Gy.P. Gehér, and D. Virosztek)

6. Isometric study of Wasserstein spaces - the real line
Transactions of the American Mathematical Society, 2020
DOI: https://doi.org/10.1090/tran/8113 (with Gy.P. Gehér, and D. Virosztek)

7. Operators on anti-dual pairs: Generalized Krein-von Neumann extension
Mathematische Nachrichten, 2020
https://doi.org/10.1002/mana.201800431 (with Zs. Tarcsay)

8. Operators on anti-dual pairs: Self-adjoint extensions and the strong Parrott theorem
Canadian Mathematical Bulletin, 2020
DOI: https://doi.org/10.4153/S0008439520000065

9. On isometric embeddings of Wasserstein spaces - the discrete case
Journal of Mathematical Analysis and Applications, 2019
DOI: https://doi.org/10.1016/j.jmaa.2019.123435 (with Gy.P. Gehér, and D. Virosztek)

10. Arlinskii's iteration and its applications
Proceedings of the Edinburgh Mathematical Society, 2019
DOI: https://doi.org/10.1017/S0013091518000287

11. A characterisation of isometries with respect to the Lévy-Prokhorov metric
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 2019
DOI: 10.2422/2036-2145.201702_011 (with Gy.P. Gehér)

12. The singular part as fixed point,
The American Mathematical Monthly, 2018
DOI: 10.1080/00029890.2018.1393219

13. A Simple Proof of the Lebesgue Decomposition Theorem
The American Mathematical Monthly, Taylor&Francis, 2015
DOI: 10.4169/amer.math.monthly.122.8.793

14. A Radon-Nikodym type theorem for forms,
Positivity, 2013
DOI: https://doi.org/10.1007/s11117-012-0209-1 (with Z. Sebestyén)

15. Ando's theorem for nonnegative forms
Positivity, 2012
DOI: https://doi.org/10.1007/s11117-011-0133-9

Selected talks

21/11/2017 Lebesgue- and Radon--Nikodym type theorems
Formal Sciences Seminar, IST Austria 
Klosterneuburg, Austria

28/11/2017 Extension of suboperators and the generalized Schur complement
Functional Analysis Seminar, University of Oxford 
Oxford, United Kingdom

19/06/2018 Characterisations of isometries with respect to probability distances
Preservers: Modern Aspects and New Directions, Queen’s University Belfast
Belfast, Northern Ireland

19/12/2018 Positive operators on anti-dual pairs
2018 China-Korea International Conference on Matrix Theory with Applications, Shanghai University
Shanghai, China

On the isometry group of metric spaces of probability measures
Researches on isometries as preserver problems and related topics, Kyoto RIMS
, Japan

08-12/07/2019 Positive operators on anti-dual pairs: Parallel addition
ILAS 2019 - Invited Mini-Symposium: Matrix Analysis
Rio de Janeiro, Brasil

17/02/2020 Isometries of Wasserstein spaces
Rings, Modules and Matrices Seminar, Lomonosov Moscow State University
Moscow, Russia

17/11/2020 Isometries of Wasserstein spaces
Analysis Seminar, University of Wisconsin-Madison
Madison, US

20-26/06/2021 Maps preserving absolute continuity of positive operators
8th European Congress of Mathematics, MS: Recent Developments on Preservers
Portoroz, Slovenia

23/11/2022 On the Monge-Kantorovich distance over concave base spaces
Real and Abstract Analysis Seminar, Charles University
Prague, Czech Republic

18/09/2023 On exotic isometries of Wasserstein spaces
Séminaire de Mathématiques et Colloquium, Institut de Recherche en Informatique, Mathématiques, Automatique et Signal
Mulhouse, France

20/09/2023 Isometries of Wasserstein spaces and Lipschitz-free spaces
Æsy to define, Hard to analyse: First conference on Lipschitz-free spaces, Centre Diocésain
Besançon, France

Ph. D. Thesis

Decomposition theory of forms, 2016
Doctoral School of Mathematics, Eötvös Loránd University


- Public body of the Hungarian Academy of Sciences

- János Bolyai Mathematical Society

- European Mathematical Society

- American Mathematical Society

Workshop and seminar organization

Thematic semester at Erdős Cender (2022 Fall, Sept-Dec): Optimal Transport on Quantum Structures
(with J. Maas, S. Rademacher and D. Virosztek)

Functional Analysis and Operator Theory Webinar – with an emphasis on preserver problems and quantum information, 2020-21
(with Gy.P. Gehér and D. Virosztek)

Preserver Webinar - an online seminar series on preserver problems, 2020
(with Gy.P. Gehér and D. Virosztek)

Analysis Seminar of the Alfréd Rényi Institute of Mathematics, 2019-2020

Preserver Weekend in Szeged, 2019
(with L. Molnár)