Dr. Athanasios Georgiadis

Assistant Professor, Statistics

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

Biography

I am an Assistant Professor in the School of Computer Science and Statistics of Trinity College of Dublin and the course Director of the Major in Mathematics with Minor in Statistics. I Studied with distinctions in Aristotle University of Thessaloniki, Greece and I obtained my PhD in 2011. Since then I have worked in 5 Universities in 4 Countries, as lecturer, postdoc and assistant professor. I have published over 30 peer-reviewed journal papers, in journals like Bernoulli, Applied and Computational Harmonic Analysis, Transactions of AMS, Journal of Nonparametric Statistics and Constructive Approximations. My main interest is in the development of function spaces in the areas of mathematical analysis and statistics. My main statistical interest is 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 my recent works, (one published in Bernoulli- between the top journals in the area) my co-authors and I established estimators via kernels and wavelets on broad metric spaces, proving optimality and adaptivity, breaking the ground for future research. Recently we applied the above estimators in the field of Seismology. Currently, I'm expanding my research horizons in neural networks, artificial intelligence and business analytics. 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. I have supervised more than 30 theses for graduate and undergraduate Students and currently I am supervising two PhD thesis (one externally funded by TikTok). I have been decisively involved in many other aspects of the Academic life, such us the organization of events like conferences, committees, teaching curriculum, exchange and more. Finally I have served the research community by refereeing more than 100 manuscripts for more than 25 journals and as a session chair in the research conferences on my fields of interest.

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, 18, (1), 2024, p1394 - 1435Journal Article, 2024
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, 2024, p1 - 30Journal Article, 2024
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
Athanasios G. Georgiadis, George Kyriazis, P. Petrushev, SPACES OF DISTRIBUTIONS ON PRODUCT METRIC SPACES ASSOCIATED WITH OPERATORS, 2024, 1 - 102ppBook, 2024

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.

Earth and related environmental sciences, Atmospheric sciences, Geoinformatics, Mathematical Sciences, Oceanography,

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