Since 2018, I am working as Distinguished Researcher at Universidad de Cádiz, on leave from a tenured position at Universidad Complutense de Madrid. From 2013-2018, I was a member of ICMAT, where I served in the Severo Ochoa Executive Committee and I helped to design the knowledge transfer strategy of the Institute. Previously, I held full-time research positions at McGill University and Centre de Recherches Mathématiques in Montréal, Università di Bologna (Marie Curie) and Universitat Politécnica de Catalunya (RyC contract).
My research interests span a wide range of topics around mathematical modeling of real world problems, approximation theory, mathematical physics, complex systems, data science and machine learning. My best known contribution to orthogonal polynomials and approximation theory has been the discovery (with N.Kamran and R. Milson) of exceptional polynomials, a class of orthogonal polynomials that are eigenfunctions of a Sturm-Liouville problem and extend the classical families of Hermite, Laguerre and Jacobi. I have investigated the theory of Darboux transformations on differential operators and its application to rational solutions of Painlevé equations.
For the past 8 years, I have been involved in knowledge transfer activities.
In Cádiz I founded and currently served as Head of UCA Datalab, a data science lab that has attracted 1.6M EUR in competitive research funds and contracts with industry, including large companies like Navantia or Airbus.
I have coordinated 8 contracts with industrial partners on specific applications of data science, mathematical modeling, Machine Learning and Natural Language Processing to diverse sectors like fisheries, healthcare, industry 4.0, insurtech, precision marketing and legaltech.
Two young teams coordinated by me have won the 2021 Ocean Hackathon (Smart Shipping project) and the 2021 OpenCV AI Competition (NeoCam project).
I have taught doctorate and masters courses at IE Business School.
Together with 2 former PhD students and 2 postdocs at ICMAT, we founded a spinoff called Komorebi AI, which has 8 employees now and excellent growth prospects.
At the Spanish Royal Mathematical Society (RSME), I am Chair of the Knowledge Transfer Commission and serve in its Governing Board. During the COVID outbreak, I served in the experts panel created by CEMat and collaborate with the Spanish Ministry of Health in assessing the efficiency of Non Pharmaceutical Interventions on the spread of the pandemics, via mathematical modeling and data analysis.
Regarding science dissemination, I co-authored a book on Big data published by CSIC, delivered public lectures at numerous events, written articles for mainstream spanish journals (El País, ABC), participated in interviews and round tables for printed media, radio and TV, either as an expert in debates or directly explaining featured projects.
- D. Gómez窶振llate, Y. Grandati, R. Milson, Complete classification of rational solutions of A2n-Painlevé systems. Adv. in Math., 385 107770, (2021).
- P. Clarkson, D. Gómez窶振llate, Y. Grandati, R. Milson, Cyclic Maya diagrams and rational solutions of higher Painlevé systems. Studies in Appl. Math., 144(3) 357-385, (2020).
- M. A. García-Ferrero, D. Gómez-Ullate, R. Milson, A Bochner type classification theorem for exceptional orthogonal polynomials, J. Math. Anal. Appl., 472 584-626, (2019).
- V. Gallego, P. Angulo, P. Suárez-García, D. Gómez-Ullate, Assessing the effect of advertising expenditures upon sales: a Bayesian structural time series model, Applied Stochastic Models in Business and Industry (2018),
- M.A. García-Ferrero, D. Gómez-Ullate, Oscillation theorems for the Wronskian of eigenfunctions of Schrödinger's equation, Lett. Math. Phys.105 551–573, (2015).
- D. Gómez-Ullate, Y. Grandati and R. Milson, Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials, J. Phys. A 47 015203, (2014)
2016 Best Paper Prize from Journal of Physics A - P. Suárez-García and D. Gómez-Ullate, Multifractality and long memory of a financial index, Physica A, 394 226–234, (2014).