報告題目：Harmonic functions and their analogues in inverse problems
報 告 人：Mikko Salo，University of Jyväskylä Professor
報告時間：2024年4月24日15:00-16:00
報告地點：Zoom link：626 9972 8466
校内聯系人：馬世琪 mashiqi@jlu.edu.cn
報告摘要：Harmonic functions describe equilibrium states in physical systems such as heat and fluid flow, electricity and gravitation. Similar objects appear in geometry as solutions of the Laplace-Beltrami, eigenfunction or Schrödinger equations on a Riemannian manifold. Various diffuse imaging methods can be modelled by the Laplace equation and its variants. This gives rise to inverse problems where the properties of an unknown medium are reconstructed from boundary measurements of solutions. A prototypical problem of this type is the inverse conductivity problem, also known as the Calderón problem, arising in electrical and seismic imaging.
This talk will give an overview of how certain harmonic functions and their counterparts have been used in the solution of inverse problems. We will describe the currently known results with an emphasis on the geometric case. We will also state several open questions.
報告人簡介：Professor Mikko Salo is a prominent mathematician from Finland known for his groundbreaking work in the field of inverse problems in partial differential equations. Professor Salo has published more than one hundred papers in prestigious journals, such as Inventiones mathematicae, Advances in Mathematics, Duke Mathematical Journal. Professor Salo won the Calderon Price in 2013, which is recognized as the highest honor in the field of inverse problems.
