"Another big challenge is to prove that we can successfully face the objectives that are proposed by us in the project, and to do so in a timely and efficient way"

Dr. Ioannis Parissis and Dr. Pedro Caro are the researchers carrying out the scientific project in theoretical mathematics that addresses the limits of current technology and proposes to advance it

Dr. Ioannis Parissis, Ikerbasque researcher associate at UPV/EHU and Dr. Pedro Caro, Ikerbasque researcher associate at BCAM, have obtained one of the grants by the Spanish Research Agency on the “PID 2021” call to develop their project. The main objective of “Interplays between Harmonic Analysis and Inverse Problems (IHAIP)” is to identify the major challenges in the areas corresponding to harmonic analysis and inverse problems, proposing problems that will advance knowledge and the current state of the art. 

“There are specific objectives in each area that are designed to do that, in harmonic analysis in problems in the interaction of geometry, analysis and combinatorics, and around the circle of problems related to the Kakeya conjecture” states Ioannis Parissis.

A very interesting aspect of the project is the interaction between different areas of mathematics (analysis, geometry, combinatorics, partial differential equations, functional analysis, algebraic geometry and differential geometry) that is underlying the statement and study of the research questions in hand. Another challenging aspect of the work is formulating the right questions, “that will help us take a step towards understanding these deep problems, but are tractable and within reach within the three year period of the project, so that some advancement will be realistic” explains Parissis. 

This is a theoretical mathematics project, specially for the harmonic analysis area, the implications and applications are also theoretical in nature. Thanks to the theorems that are going to be developed within the project, they would achieve additional insight about related families of problems, or obtain direct applications to other theoretical questions. Parissis highlights that the inverse problem part of the project “is philosophically closer to real life applications, and the framework of the project is very relevant in tomography techniques.

The researchers explain that the project has important implications for the training of PhD students and young postdoctoral researchers: “Through this and previous such projects we have managed to attract several people to come and work with us in Bilbao, on the one hand in terms of getting training within our group, but on the other hand also more senior mathematicians have decided to join our group“. 

These contributions are often underestimated, but they have great impact on the local mathematical-scientific environment. The visibility of the joint analysis and EDP group in the UPV/EHU and BCAM has improved, and a very solid base has been established for the development of the relevant scientific fields in the Basque Country.

“The selection of our project, with a good outcome in terms of ranking and total funding, is a recognition of our work and efforts during the previous years, and also an encouragement to continue in the directions of research that we have chosen. It shows that we have established these lines of research as important in the community, and that we have also gained the trust of our peers that we are in the position to successfully pursue them”, conclude Dr. Parissis and Dr. Caro.

From now on, the big challenge for Caro and Parissis will be to continue like this over the long term, “another big challenge is to prove that we can successfully face the objectives that are proposed by us in the project, and to do so in a timely and efficient way. This will allow us to formulate follow up questions, to have even more evidence that our research strategy was well thought off and constructive for scientific development, and to be successful in future project proposals”.


About the researchers

Dr. Ioannis Parissis graduated with a PhD in 2007 from the University of Crete (Greece) and he has been researching as a Postdoctoral Fellow  in the USA and Europe. He is an Ikerbasque researcher at UPV/EHU and he collaborates with researchers at UPV/EHU and at BCAM as well as internationally. Also he is supervising one PhD Student at BCAM.

Dr. Pedro Caro graduated as a PhD from the Universidad Autónoma de Madrid after studying a Bachelor Degree in Mathematics in Seville and a Masters’ Degree in Paris. He is an Ikerbasque Research Fellow at BCAM and mainly works on inverse problems arising in the study of Partial Differential Equations. His research interests also include mathematical analysis and its applications.