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



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)
  • School: Sept 19-23, 2022 [poster]
    Lecturers:
    E.A. Carlen (Rutgers University), A. Figalli (ETH Zurich), F. Golse (CMLS Ecole Polytechnique), D. Trevisan (University of Pisa)
  • Workshop: Sept 26-30, 2022 [poster]
    Invited speakers: P. Antonini (Università del Salento), Z. Balogh (University of Bern), Y. Brenier (Universite Paris-Saclay),
    A. Capel (Universität Tübingen),
    E. Caglioti (Sapienza University of Rome), Li Chen (University of Mannheim, Germany),
    N. Datta (University of Cambridge), G. De Palma (University of Bologna),
    M. Eckstein (Jagiellonian University), M. Iacobelli (ETH Zurich),
    L. Lafleche (UT Austin),
    L. Portinale (Hausdorff Center for Mathematics Bonn), C. Rouzé (TU Munich), D. Shlyakhtenko (UCLA),
    M. Wirth (IST Austria)
    H. Zhang (IST Austria), K. Zyczkowski (Polish Academy of Sciences)

  • Focus event on Modified Logarithmic Sobolev Inequalities for Quantum Markov Semigroups: November 21-25, 2022
    Ivan Bardet (Inria de Paris, France) Angela Capel (Universität Tübingen, Germany)
    Cambyse Rouzé (Technische Universität München, Germany), Daniel Stilck França (ENS Lyon, France)

  • Focus Event on the Geometry of Wasserstein Spaces: November 28 - December 2, 2022
    Ramón J. Aliaga (Universitat Politècnica de València), Zoltán Balogh (University of Bern, Switzerland)
    Nicolas Juillet (Université de Haute-Alsace), Eva Pernecká (Czech Technical University in Prague)


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)



Editorial work


2019-    Editor of Periodica Mathematica Hungarica

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



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)



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 (to appear), 2022
arXiv:2203.04054
(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



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