# Program

Inverse problems (IP) arise in all fields of science and technology where a cause for an observed or desired effect is sought. In the last 50 years or so there has been substantial progress in the mathematical understanding of these problems but many questions remain open. The mathematics of these problems involves many areas in Mathematics including PDE, differential geometry, integral geometry, probability, statistics, complex analysis, numerical analysis, mathematical physics, data science, etc. Since the 2010 program at the then-Mathematical Sciences Research Institute (now Simons Laufer Mathematical Sciences Institute), there has been significant progress in inverse problems; many of the advances can be traced back to that program. However, there are still deep open questions remaining as well, some of which are discussed in this proposal. New research topics include the connection between IP and machine learning, IP for nonlinear equations, IP for nonlocal operators, and connections between statistics and IP.

**Keywords and Mathematics Subject Classification (MSC)**

**Tags/Keywords**

inverse problems

Microlocal analysis

partial differential equations

Calder´on’s problem

lens and boundary rigidity

scattering theory

transmission eigenvalues

resonances

quantum chaos

singular spaces

general relativity

quantum field theory

and machine learning.

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**No Secondary AMS MSC