Dr. Athanasios Georgiadis

Assistant Professor, Statistics

georgiaa@tcd.ie https://sites.google.com/site/nasosmath/

Biography

I am a tenure track Assistant Professor in the School of Computer Science and Statistics of Trinity College of Dublin and the module co-ordinator of the Minor in Statistics. I was born in Athens, Greece in August 14th of 1984, I am married and Father of a Son. I Studied with distinctions in Aristotle University of Thessaloniki, Greece and I obtained my PhD in 2011. Since then I have worked in five Universities in four Countries, as teaching assistant, lecturer, post-doctoral associate and assistant professor. I have published 29 peer-reviewed journal papers, in journals like Bernoulli, Journal of Nonparametric Statistics, Stochastic Processes and Applications, Applied and Computational Harmonic Analysis, Transactions of AMS, my PhD thesis and I have co-authored 2 peer-reviewed articles for conferences' proceedings. My main interest is in the use of function spaces in statistics and pure mathematics. Precisely I am interesting in exploring estimation of probability density functions and approximation of random fields. One of my main achievements is the estimation of probability density functions of random variables distributed on manifolds and more general metric spaces. In the two recent works, published in Bernoulli (one of the top journals in Statistics) and in the Journal of Nonparametric Statistics (the most standard venue in my research area) my co-authors and I proposed estimators constructed by kernels and wavelets. We proved that our objects are rate optimal and adaptive. We already attracted the attention of the community of Nonparametric Statistics and we built the ground for future research. Recently we applied the above estimators in the field of Seismology. I have concrete and ambitious plans for the future that involve the development of function spaces on general geometric settings and their use for the study of spatial and spatiotemporal phenomena. Moreover, I'm expanding my research interests in other fields, like neural networks and I am scheduling my entrance in this research area, too. Note also that in the several projects above, I am already in discussions and collaborations with some of the top researchers in the particular research fields. As a teacher, I have the experience of teaching in 5 different Universities, in all the types of audiences with respect to the size, age and background and I always receive excellent reports from my students. The biggest moment in my teaching career was in 2017 when I was awarded as the "Teacher of the year" in Aalborg University, Denmark, between more than 400 lectures. I have supervised more than 20 theses for both graduate and undergraduate Students as well as summer internships and currently I am supervising a PhD thesis externally funded by TikTok. I have been decisively involved in many other aspects of the Academic life, such us the organization of events, the participation in committees, the update of teaching material and more. My main current duties include the co-ordination of the Minor in Statistics offered by the SCSS. Finally I have served the research community by refereeing more than 100 manuscripts for more than 20 journals and in the summer of 2022 I had my own session chair in the most important event in Nonparametric Statistics; the International Symposium on Nonparametric Statistics.

Publications and Further Research Outputs

Peer-Reviewed Publications

G. Cleanthous, A. G. Georgiadis, A. Lang and E. Porcu, Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces, Stochastic Processes and their Applications, 130, (8), 2020, p4873 - 4891Journal Article, 2020
G. Cleanthous and A. G. Georgiadis, Mixed-norm $\alpha$-modulation spaces, Transactions of AMS, 373, (5), 2020, p3323 - 3356Journal Article, 2020
G. Cleanthous, A. G. Georgiadis, G. Kerkyacharian, P. Petrushev, D. Picard, Kernel and wavelet density estimators on manifolds or more general metric spaces, Bernoulli, 26, (3), 2020, p1832-1862Journal Article, 2020
A. G. Georgiadis, G. Kyriazis, P. Petrushev, Product Besov and Triebel-Lizorkin spaces with application to nonlinear approximation, Constructive Approximation, 53, 2021, p39 - 83Journal Article, 2021
A. G. Georgiadis, G. Kerkyacharian, G. Kyriazis and P. Petrushev, Atomic and molecular decomposition for homogeneous spaces of distributions associated to non-negative self-adjoint operators, Journal of Fourier Analysis and Applications, 25, (6), 2019, p3259-3309Journal Article, 2019
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel-Lizorkin spaces, Monatshefte für Mathematik, 188, (3), 2019, p467-493Journal Article, 2019
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators, Applied and Computational Harmonic Analysis, 47, (2), 2019, p447-480Journal Article, 2019
A. G. Georgiadis, and M. Nielsen, Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators, Journal of Approximation Theory, 234, 2018, p1-19Journal Article, 2018
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Fourier multipliers on anisotropic mixed-norm spaces of distributions, Mathematica Scandinavica, 124, (2), 2019, p289-304Journal Article, 2019
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Fourier multipliers on decomposition spaces of Modulation and Triebel-Lizorkin type, Mediterranean Journal of Mathematics, 15, (3), 2018, p122-Journal Article, 2018
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Anisotropic mixed-norm Hardy spaces, The Journal of Geometric Analysis , 27, (4), 2017, p2758-2787Journal Article, 2017
A. G. Georgiadis, and M. Nielsen, Pseudodifferential operators on spaces of distributions associated with non-negative self-adjoint operators, Journal of Fourier Analysis and Applications, 23, (2), 2017, p344-378Journal Article, 2017
A. G. Georgiadis, G. Kerkyacharian, G. Kyriazis and P. Petrushev, Homogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators, Journal of Mathematical Analysis and Applications, 449, (2), 2017, p1382-1412Journal Article, 2017
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Discrete decomposition of homogeneous mixed-norm Besov spaces, Contemporary Mathematics AMS, 693, 2017, p167-184Journal Article, 2017
A. G. Georgiadis, J. Johnsen and M. Nielsen, Wavelet transforms for homogeneous mixed-norm Triebel-Lizorkin spaces, Monatshefte für Mathematik, 183, (4), 2017, p587 - 624Journal Article, 2017
A. G. Georgiadis, and M. Nielsen, Pseudodifferential operators on mixed-norm Besov and Triebel-Lizorkin spaces, Mathematische Nachrichten, 289, (16), 2016, p2019-2036Journal Article, 2016
G. Cleanthous and A. G. Georgiadis, Riesz means via heat kernel bounds, Bulletin of Hellenic Mathematical Society, 60, 2016, p1-10Journal Article, 2016
G. Cleanthous and A. G. Georgiadis, Growth and monotonicity properties for elliptically schlicht functions, Conformal Geometry and Dynamics of the American Mathematical Society, 20, (7), 2016, p116-127Journal Article, 2016
G. Cleanthous and A. G. Georgiadis, Upper and lower estimates for the modulus of bounded holomorphic functions, Complex Analysis and Operator Theory, 10, (1), 2016, p205-212Journal Article, 2016
A. G. Georgiadis, Oscillating spectral multipliers on Riemannian manifolds, Analysis Munchen, 35, (2), 2015, p85-91Journal Article, 2015
G. Cleanthous and A. G. Georgiadis, Multi-point bounds for analytic functions under measure conditions, Complex Variables and Elliptic Equations, 60, (4), 2015, p470-477Journal Article, 2015
A. G. Georgiadis and A. Fotiadis, Riesz means on discrete groups and graphs, Potential Analysis, 38, (1), 2013, p21-30Journal Article, 2013
A. G. Georgiadis, Mikhlin-Hormander theorem for higher order differential operators on Riemannian manifolds, Journal of Mathematical Sciences: Advances and Applications, 7, (2), 2011, p115-132Journal Article, 2011
A. G. Georgiadis, $H, p$- bounds for spectral multipliers on Riemannian manifolds, Bulletin des sciences mathematiques, 134, (7), 2010, p750-766Journal Article, 2010
A. G. Georgiadis, Analysis on metric spaces associated with operators II, 90 Years School of Mathematics AUTH Proceedings, Anniversary for the 90 years of Math. Dept. Auth., Department of Mathematics, Aristotle University of Thessaloniki, Greece, December 2018, 2018, pp115-127Conference Paper, 2018
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Spaces of distributions with mixed Lebesgue norms, Proceedings of the 15th Panhellenic conference of mathematical analysis, 15th Panhellenic conference of mathematical analysis, Department of Mathematics and Applied Mathematics, University of Crete, Greece, May 2016, 2016, pp29-38Conference Paper, 2016
A. G. Georgiadis, Spectral multipliers and Riesz means on manifolds, groups and graphs, 2011Thesis, 2011
G. Cleanthous, A. G. Georgiadis and E. Porcu, Oracle inequalities and upper bounds for kernel density estimators on manifolds or more general metric spaces, Journal of nonparametric statistics, 34, (3), 2022, p734 - 775Journal Article, 2022
G. Cleanthous and A. G. Georgiadis, Product $(\alpha_1,\alpha_2)$-modulation spaces, Science China Mathematics, 65, (8), 2022, p1599 - 1640Journal Article, 2022
A. G. Georgiadis and G. Kyriazis, Embeddings for Triebel-Lizorkin spaces associated with operators, Analysis and Geometry on Metric spaces, 8, (1), 2021, p418 - 429Journal Article, 2021
A. Alegria, G. Cleanthous, A. G. Georgiadis, E. Porcu, P. White, Gaussian random fields on the product of spheres: theory and applications, Electronic Journal of Statistics, 2023Journal Article, 2023
A. G. Georgiadis and G. Kyriazis, Duals of Besov spaces on metric spaces associated with operators, Constructive Approximations, 57, (2), 2023, p547 - 577Journal Article, 2023
Galatia Cleanthous, Athanasios G. Georgiadis, Philip White, Pointwise density estimation on metric spaces and applications in seismology, Metrika, 2023Journal Article, 2023
George Filippou, Athanasios G. Georgiadis, Ashish Kumar Jha, Establishing the link: Does web traffic from various marketing channels influence direct traffic source purchases?, Marketing letters, 2023, p1-13Journal Article, 2023

My primary interests center on Nonparametric and Spatial Statistics. Specifically, I am focused on the estimation of probability density functions in Euclidean spaces, spheres, balls, and general manifolds. Nonparametric estimation in this context necessitates the development of sophisticated mathematical tools, including smoothness spaces and wavelets, which is an aspect that particularly captivates my attention. One of my significant contributions in this field involves the estimation of the density of random variables distributed on general manifolds using kernels and wavelets. This work represents a generalization of some of the most prominent results in the field and has been published in the prestigious Bernoulli journal, known as one of the top statistical journals, and the Journal of Nonparametric Statistics, which is dedicated to this research area. In Spatial Statistics, my work centers on the behavior of random fields, encompassing aspects like regularity, continuity, simulations, and approximation. This research requires a deep theoretical foundation and holds of fundamental importance in the areas of Cosmology, Environmental Science and more. I have applied my theoretical developments and statistical expertise in various fields, including Seismology, Climatology, and, more recently, Business Analytics. I am continuously seeking to broaden my horizons and venture into new scientific domains. Presently, I am in initial discussions about the application of statistical methods in Neural Networks, with the expectation of making progress in this direction over the next few years. My future plans are twofold: to delve deeper into the areas I've mentioned, both in terms of establishing new theorems and applying my developments to practical scientific challenges. I plan to focus on (a) product spaces, (b) manifolds, and (c) graphs in my upcoming research. These plans have garnered the interest of established scientists, and we aim to collaborate on advancing these developments together.

Environmental and geological engineering, geotechnics;, Environmental Sciences including Marine, Air Quality, Environment (incl.) Climate Change, Mathematics,

Recognition

Funding for PhD thesis, from Onassis' Foundation, Greece. 2008-2011
Award for excellent performance in graduate studies 2006-2008
Teacher of the Year, School of Engineering and Science, Aalborg University, Denmark. 2017-2018
Performance Scholarship during every year of the graduate studies 2006-2008
Award for excellent performance in diploma studies 2002-2006
Funding for graduate studies, from Onassis' Foundation, Greece 2006-2008
Performance Scholarship during every year of the undergraduate studies 2002-2006

Zentralblatt math. Reviewer number: 14491
American mathematical society. Reviewer number: 74550

Organizer of the daily conference: "A day with Analysis, Geometry and Statistics". Department of Mathematical Sciences, Aalborg University, Denmark. 2017
UCAO-Joint honours coordinators 2022-
Organizer of the conference: "Marie Curie International Fellows' talks in Aalborg". Department of Mathematical Sciences, Aalborg University, Denmark. 2017
Founder and organizer of the departmental seminar in Department of Mathematical Sciences, Aalborg University, Denmark. 2016-2017
Organizing Committee for the event: TCD Symposium in Statistics 2023
Reviewer for Zbmath. Reviewer number: 14491. 2013-2023
Course director: Major in Mathematics with a Minor in Statistics 2022-
Anonymous Referee for 28 journals for more than 150 manuscripts. 2011-2023
Undergraduate Teaching and Learning Committee, TCD 2022-
Invited session organizer on the conference: "International Symposium in Non Parametric Statistics 2022". June 2022
Reviewer for AMS. Reviewer number: 74550. 2010-2023