Dr. Athanasios Georgiadis
Assistant Professor, Statistics
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
Galatia Cleanthous, Athanasios G. Georgiadis and G. Kyriazis, Frame Decomposition of Mixed-Smoothness Besov and Triebel-Lizorkin Spaces on Product Metric Spaces Associated to Operators, Journal of Fourier Analysis and Applications, 32, (38), 2026, p1 - 72
Athanasios G. Georgiadis and Andrew P. Percival, Rate-optimal and computationally efficient nonparametric density and probability estimation on the circle and the sphere., Electronic Journal of Statistics, 20, (2), 2026, p3255 - 3290
Alfredo Alegría, Galatia Cleanthous and Athanasios G. Georgiadis, Series expansion and fast simulations of multivariate isotropic random fields on the paraboloid, Computational and Applied Mathematics, 45, (152), 2026, p1 - 19
Athanasios G. Georgiadis, George Kyriazis, Pencho Petrushev, Spaces of Distributions on Product Metric Spaces Associated with Operators, Dissertationes Mathematicae, 2025, 1 - 114pp
Galatia Cleanthous, Athanasios G. Georgiadis, Oleg V. Lepski, Adaptive Estimation of the L_2-Norm of a Probability Density and Related Topics II. Upper Bounds via the Oracle Approach, Annals of Statistics, 53, (3), 2025, p1275 - 1297
George Filippou, Athanasios G. Georgiadis, Ashish Kumar Jha, Unveiling digital dynamics: Do digital media investments impact organic branded searches?, Journal of Marketing Analytics, 2025, p1-13
Galatia Cleanthous, Athanasios G. Georgiadis, Oleg V. Lepski, Adaptive Estimation of the L_2-Norm of a Probability Density and Related Topics I. Lower Bounds, Annals of Statistics, 53, (3), 2025, p1257 - 1274
Galatia Cleanthous, Athanasios G. Georgiadis, Philip White, Pointwise density estimation on metric spaces and applications in seismology, Metrika, 2024, p1 - 30
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 - 1435
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, (35), 2024, p59-71
A. G. Georgiadis and G. Kyriazis, Duals of Besov spaces on metric spaces associated with operators, Constructive Approximations, 57, (2), 2023, p547 - 577
G. Cleanthous and A. G. Georgiadis, Product $(\alpha_1,\alpha_2)$-modulation spaces, Science China Mathematics, 65, (8), 2022, p1599 - 1640
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 - 775
A. G. Georgiadis and G. Kyriazis, Embeddings for Triebel-Lizorkin spaces associated with operators, Analysis and Geometry on Metric spaces, 8, (1), 2021, p418 - 429
A. G. Georgiadis, G. Kyriazis, P. Petrushev, Product Besov and Triebel-Lizorkin spaces with application to nonlinear approximation, Constructive Approximation, 53, 2021, p39 - 83
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, p1832-1862
G. Cleanthous and A. G. Georgiadis, Mixed-norm $\alpha$-modulation spaces, Transactions of AMS, 373, (5), 2020, p3323 - 3356
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 - 4891
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, p3259-3309
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, p467-493
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, p447-480
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Fourier multipliers on anisotropic mixed-norm spaces of distributions, Mathematica Scandinavica, 124, (2), 2019, p289-304
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-
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, p1-19
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, pp115-127
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Discrete decomposition of homogeneous mixed-norm Besov spaces, Contemporary Mathematics AMS, 693, 2017, p167-184
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, p1382-1412
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, p344-378
G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Anisotropic mixed-norm Hardy spaces, The Journal of Geometric Analysis , 27, (4), 2017, p2758-2787
A. G. Georgiadis, J. Johnsen and M. Nielsen, Wavelet transforms for homogeneous mixed-norm Triebel-Lizorkin spaces, Monatshefte für Mathematik, 183, (4), 2017, p587 - 624
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, p205-212
G. Cleanthous and A. G. Georgiadis, Riesz means via heat kernel bounds, Bulletin of Hellenic Mathematical Society, 60, 2016, p1-10
A. G. Georgiadis, and M. Nielsen, Pseudodifferential operators on mixed-norm Besov and Triebel-Lizorkin spaces, Mathematische Nachrichten, 289, (16), 2016, p2019-2036
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, p116-127
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, pp29-38
A. G. Georgiadis, Oscillating spectral multipliers on Riemannian manifolds, Analysis Munchen, 35, (2), 2015, p85-91
G. Cleanthous and A. G. Georgiadis, Multi-point bounds for analytic functions under measure conditions, Complex Variables and Elliptic Equations, 60, (4), 2015, p470-477
A. G. Georgiadis and A. Fotiadis, Riesz means on discrete groups and graphs, Potential Analysis, 38, (1), 2013, p21-30
A. G. Georgiadis, Mikhlin-Hormander theorem for higher order differential operators on Riemannian manifolds, Journal of Mathematical Sciences: Advances and Applications, 7, (2), 2011, p115-132
A. G. Georgiadis, Spectral multipliers and Riesz means on manifolds, groups and graphs, 2011
A. G. Georgiadis, $H, p$- bounds for spectral multipliers on Riemannian manifolds, Bulletin des sciences mathematiques, 134, (7), 2010, p750-766
Research Expertise
Description
My research lies at the intersection of Mathematical Analysis and Statistics. A distinctive feature of my programme is the interaction between these areas: I develop mathematical theory to address fundamental statistical problems, increasingly translating it into practical methods and interdisciplinary applications. My most significant recent achievement is the resolution of a long-standing open problem in adaptive estimation, through two consecutive papers in the Annals of Statistics, the leading international journal in Statistics. The problem concerns optimal adaptive estimation of the L2-norm of an unknown probability density and had remained open for approximately three decades. This fundamental quantity is connected to major statistical problems, including goodness-of-fit testing, confidence sets and information-theoretic measures such as entropy, and arises in regression, cross-validation, signal processing and inverse problems. We established matching lower and upper bounds, providing a sharp and complete problem solution, while developing new theoretical tools and frameworks with broader applicability. To the best of my knowledge, these are the first Annals of Statistics publications by Ireland-based researchers. A second major achievement is my recent 114-page research monograph in Dissertationes Mathematicae, developing a comprehensive theory of product smoothness spaces on metric spaces, allowing different structures and smoothness properties across individual variables. This represents a substantial contribution to Mathematical Analysis and provides foundations for future developments in Statistics on complex domains. These achievements build on a 15-year sustained record of theoretical contributions, to operators and function spaces, nonparametric estimators, and random fields, published in leading international journals such as Bernoulli, Transactions of the American Mathematical Society, Applied and Computational Harmonic Analysis, and the Journal of Fourier Analysis and Applications. My research increasingly extends from theory to application, spanning Astronomy, Business Analytics, Climatology, Environmental Science, Seismology, and Zoology. My future programme builds on these achievements through ambitious theoretical problems, international collaborations and expanding interdisciplinary applications.Recognition
Representations
Journal Referee
Reviewer for AMS. Reviewer number: 74550.
Reviewer for Zbmath. Reviewer number: 14491.
Awards and Honours
Teacher of the Year, School of Engineering and Science, Aalborg University, Denmark.
Award for excellent performance in diploma studies
Award for excellent performance in graduate studies
Performance Scholarship during every year of the undergraduate studies
Performance Scholarship during every year of the graduate studies
Funding for PhD thesis, from Onassis' Foundation, Greece.
Funding for graduate studies, from Onassis' Foundation, Greece
Memberships
Czech Science Foundation (GACR), Czech Republic - International Referee / Grant Reviewer.
American mathematical society. Reviewer number: 74550
Zentralblatt math. Reviewer number: 14491