Tamás TITKOS



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. 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)

2. 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)

3. Isometric rigidity of Wasserstein tori and spheres
Mathematika, 2022
DOI: https://doi.org/10.1112/mtk.12174
(with Gy.P. Gehér, and D. Virosztek)

4. 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)

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

6. 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)

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

8. 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)

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

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



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


29/01/2019
On the isometry group of metric spaces of probability measures
Researches on isometries as preserver problems and related topics, Kyoto RIMS
Kyoto
, 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



Memberships

- 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)