Non-zero Constraints in Partial Differential Equation and Applications to Hybrid Inverse Problems

Abstract

The reconstruction in quantitative coupled-physics imaging often requires that the solutions of certain Partial Differential Equations (PDEs) satisfy some non-zero constraints, such as the absence of critical points or nodal points. The speaker will review several methods that have been employed to construct such solutions, including the Radó–Kneser–Choquet theorem, complex geometrical optics solutions, the use of multiple frequencies, the Runge approximation, the Whitney embedding theorem, and the use of random boundary conditions.

About the Speaker

Prof. Giovanni ALBERTI obtained his MS from the University of Genoa in 2011 and his PhD from the University of Oxford, all in Mathematics. He was a Postdoctoral Fellow at the École Normale Supérieure – PSL in 2014-2015 and at ETH Zürich in 2015-2016. He returned to his alma mater, the University of Genoa in 2016 and is currently a tenure-track Assistant Professor at the Department of Mathematics.

Prof. Alberti’s research focuses on partial differential equations, applied harmonic analysis, and on their interactions with inverse problems, machine learning and imaging. He was the Associate Editor of Inverse Problems in Science and Engineering in 2019-2021.

Prof. Alberti is the recipient of the 2017 Premio Gioacchino Iapichino Prize in Mathematical Analysis from the Italian National Academy and the 2018 Eurasian Association on Inverse Problems Young Scientist Award from the International Conferences “Inverse Problems: Modeling and Simulation”. In 2021, he was selected for “Emerging Talents 2021” by the journal Inverse Problems.

For Attendees' Attention

This talk will be held online via Zoom. To attend, please join the Zoom meeting at https://hkust.zoom.us/j/99116590392 (Meeting ID: 991 1659 0392 / Passcode: iasip2022).

About the Program

For more information, please refer to the program website at https://iasprogram.hkust.edu.hk/inverseproblems/.