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# Dr. Athanasios Georgiadis Assistant Professor, Statistics

## 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 28 peer-reviewed journal papers, in journals like Bernoulli, Journal of Nonparametric Statistics, Stochastic Processes and Applications, Applied and Computational Harmonic Analysis, Transactions of AMS 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

Galatia Cleanthous, Athanasios G. Georgiadis, Philip White, DENSITY ESTIMATION ON METRIC SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS IN SEISMOLOGY, Journal of nonparametric statistics, 2023 Journal Article, 2023

A. G. Georgiadis and G. Kyriazis, Duals of Besov spaces on metric spaces associated with operators, Constructive Approximations, 2022 Journal Article, 2022

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 Journal Article, 2022

A. Alegria, G. Cleanthous, A. G. Georgiadis, E. Porcu, P. White, Gaussian random fields on the hypertorus: theory and applications, Electronic Journal of Statistics, 2022 Journal Article, 2022

G. Cleanthous and A. G. Georgiadis, Product $(\alpha_1,\alpha_2)$-modulation spaces, Science China Mathematics, 2022, p1 - 48 Journal 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 - 429 Journal Article, 2021

A. G. Georgiadis, G. Kyriazis, P. Petrushev, Product Besov and Triebel-Lizorkin spaces with application to nonlinear approximation, Constructive Approximation, 53, 2021, p39 - 83 Journal Article, 2021

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 Journal Article, 2020

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 Journal Article, 2020

G. Cleanthous and A. G. Georgiadis, Mixed-norm $\alpha$-modulation spaces, Transactions of AMS, 373, (5), 2020, p3323 - 3356 Journal Article, 2020

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 Journal Article, 2019

G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Fourier multipliers on anisotropic mixed-norm spaces of distributions, Mathematica Scandinavica, 124, (2), 2019, p289-304 Journal Article, 2019

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 Journal 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, p467-493 Journal 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, p1-19 Journal Article, 2018

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

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 Conference Paper, 2018

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 Journal Article, 2017

G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Anisotropic mixed-norm Hardy spaces, The Journal of Geometric Analysis , 27, (4), 2017, p2758-2787 Journal Article, 2017

G. Cleanthous, A. G. Georgiadis, and M. Nielsen, Discrete decomposition of homogeneous mixed-norm Besov spaces, Contemporary Mathematics AMS, 693, 2017, p167-184 Journal 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, p1382-1412 Journal 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, p344-378 Journal Article, 2017

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 Journal Article, 2016

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 Conference Paper, 2016

A. G. Georgiadis, and M. Nielsen, Pseudodifferential operators on mixed-norm Besov and Triebel-Lizorkin spaces, Mathematische Nachrichten, 289, (16), 2016, p2019-2036 Journal 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, p205-212 Journal Article, 2016

G. Cleanthous and A. G. Georgiadis, Riesz means via heat kernel bounds, Bulletin of Hellenic Mathematical Society, 60, 2016, p1-10 Journal Article, 2016

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 Journal Article, 2015

A. G. Georgiadis, Oscillating spectral multipliers on Riemannian manifolds, Analysis Munchen, 35, (2), 2015, p85-91 Journal Article, 2015

A. G. Georgiadis and A. Fotiadis, Riesz means on discrete groups and graphs, Potential Analysis, 38, (1), 2013, p21-30 Journal Article, 2013

A. G. Georgiadis, Spectral multipliers and Riesz means on manifolds, groups and graphs, 2011 Thesis, 2011

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 Journal Article, 2011

A. G. Georgiadis, $H, p$- bounds for spectral multipliers on Riemannian manifolds, Bulletin des sciences mathematiques, 134, (7), 2010, p750-766 Journal Article, 2010

## Research Expertise

### Description

My main interests lie in the areas of nonparametric statistics and spatial statistics. Precisely, I am interested in the estimation of probability density functions (pdf's) defined over Euclidean spaces, spheres, balls, manifolds and more general metric spaces. For the purpose of nonparametric estimation, sophisticated mathematical tools such as smoothness spaces, kernels, wavelets and other machinery has to be constructed and this fact attracts further my attention. I have also suceeded to apply my results in the area of Seismology. My most important contribution in this area was the estimation of the density of a random variable distributed on general manifolds, via kernels and wavelets. Our methods generalized the most prominent results in the field, have been rate optimal and adaptive. Indicatively I mention that the above work enjoys publication in the Bernoulli journal which is between the exceptionaly top Statistical journals and the Journal of Nonparametric Statistics (the homonym journal of the research area). Another direction that attracts my attention is spatial statistics and especially the behavior of random fields. Precisely, I have studied regularity, continuity, simulations and the approximation of random fields on several geometric settings such as spheres, compact two-point homogeneous spaces (general manifolds that include projective spaces), the hypertorus and more. This study relies deeply in the notion of covariance functions, which in turn can be explored based on the general positive-definiteness theory, which needs deep theoretical handling. The importance of the covariance functions is apparent even in problems raising in environmental science. In our works are contained the theoretical developments and applications in Environmental science and Climatology, which excites me and I will keep working hard in this direction. My main future plans include the study of both Nonparametric Statistics and Spatial Statistics on (a) product spaces (b) manifolds and (c) graphs. (a) Product spaces, appear naturally once the object under study (e.g. a pdf, or a random field) depends on more than one variables, which are of completely different nature. For example spatiotemporal phenomena, demand such a handling. (b) The data under study may be located in a variety of surfaces. Manifolds consist a very broad way to unify many geometric settings that could be of the interest in different problems. Cosmology, Enviromental science and Seismology are just a few typical examples of Sciences that demand the study of complicated geometric settings. (c) Graphs should be understood as the discretized version of manifolds. The progress in the area of big data, equipped the science with information that can be viewed as discrete graphs, substituting manifolds (mountains, parts of the human body, surfaces on planets and other sky objects) that are difficult to be handled, understood, formalized and then studied. I have concrete research plans in the above mentioned directions. My plans have already attracted the interest of some top-established scientists, with whom we will try together to succeed the developments. All the above plans are abitious and have the potential to enjoy the publication in top-ranked journals, attract the attention of the community, offer funds to my School and further establish me in my research area. Finally, I am constantly trying to expand my horizons and entering in new scientific fields. Currently I am in some first discussion about Neural Networks. I expect to see some progress in this direction during the next couple of years.

## Recognition

### Representations

Module coordinator: Major in Mathematics with a Minor in Statistics 2022-

Anonymous Referee for more than 20 journals for more than 100 manuscripts. 2011-2023

UCAO - Erasmus/Study Abroad Coordinators 2022-

Organizing Committee for the event: TCD Symposium in Statistics 2023

Reviewer for AMS. Reviewer number: 74550. 2010-2023

Reviewer for Zbmath. Reviewer number: 14491. 2013-2023

Invited session organizer on the conference: "International Symposium in Non Parametric Statistics 2022". June 2022

Organizer of the conference: "Marie Curie International Fellows' talks in Aalborg". Department of Mathematical Sciences, Aalborg University, Denmark. 2017

Organizer of the daily conference: "A day with Analysis, Geometry and Statistics". 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

### Awards and Honours

Teacher of the Year, School of Engineering and Science, Aalborg University, Denmark. 2017-2018

Award for excellent performance in diploma studies 2002-2006

Award for excellent performance in graduate studies 2006-2008

Performance Scholarship during every year of the undergraduate studies 2002-2006

Performance Scholarship during every year of the graduate studies 2006-2008

Funding for PhD thesis, from Onassis' Foundation, Greece. 2008-2011

Funding for graduate studies, from Onassis' Foundation, Greece 2006-2008

### Memberships

American mathematical society. Reviewer number: 74550

Zentralblatt math. Reviewer number: 14491