Inverse problems is a field of mathematics comprised of many areas including analysis, modeling, PDE's and scientific computation. Inverse problems arise in abundance in engineering, biology, physics, geophysics and more. This seminar addresses fundamental topics in inverse problems in a variety of applications.

Regular meeting times & location: Thursdays at 2 pm in Weber 223

Abstract: Quantum graphs are metric graphs with differential equations defined on the edges. Recent interest in control and inverse problems for quantum graphs is motivated by applications to important problems of classical and quantum physics, chemistry, biology, and engineering. In this talk we describe some new controllability and identifiability results for partial differential equations on compact graphs. In particular, we consider graph-like networks of inhomogeneous strings with masses attached at the interior vertices. We show that the wave transmitted through a mass is more regular than the incoming wave. Therefore, the regularity of the solution to the initial boundary value problem on an edge depends on the combinatorial distance of this edge from the source, that makes control and inverse problems for such systems more difficult. We prove the exact controllability of the systems with the optimal number of controls and propose an algorithm recovering the unknown densities of the strings, lengths of the edges, attached masses, and the topology of the graph. The proofs are based on the boundary control and leaf peeling methods developed in our previous papers. The boundary control method is a powerful method in inverse theory which uses deep connections between controllability and identifiability of distributed parameter systems and lends itself to straightforward algorithmic implementations.

Oct. 4 | Attend Applied Math Seminar at 3 pm, Weber 223: The Role of the Push-Forward Measure in Solving Inverse Problems: An Interactive Talk Using Jupyter Notebooks | Troy Butler, Univ. CO Denver |

Oct. 11 | Chemical-specific contrast in laser microscopy: inverse problems and nonlinear mappings | Jesse Wilson, Dept. of ECE and SBME, CSU |

Oct. 25 | Hyperspectral Synthetic-Aperture Radar | Andrew Horman, Matrix Research |

Nov. 1 | no seminar - Math Day | |

Nov. 15 | Coherent imaging with incoherent light and super-resolution imaging with spatio-temporally modulated illumination light | Randy Bartels, Dept. of ECE and SBME, CSU |

Nov. 29 | Control and Inverse Problems for Differential Equations on Graphs | Sergei Avdonin, University of Alaska Fairbanks |

[Spring 2015] [Fall 2014]