Workshop Schedule

While primarily intended for graduate students and junior faculty who may not have encountered some of these topics, the mathematical breadth of the AIP meeting itself means that many participants may also gain benefit from attendance at some of the lectures.

Registration is requested. This is primarily in order to have information to allocate such funding but also so we can place these lectures in the correct size room. As in AIP2011 itself, there is no registration fee.

All talks will be held in Blocker 113; the coffee and registration will be held in Blocker first floor foyer.

Saturday 21 May
9:00-10:00 Welcome and coffee
10:00-11:00 Charles Groetsch,
"Inverse Problems and Regularization Theory: part 1"
  • What are Inverse Problems?; Some History
  • Some Model Inverse Problems
  • A Framework for Inverse Problems
  • The Moore-Penrose Inverse
  • Compact Operators and the SVD
  • What is Regularization?
11:00-12:00 Peter Kuchment,
"Tomographic methods in Imaging; part 1"
  • A Historical Survey
  • Integral-geometric Techniques
  • PDE and Microlocal Techniques
  • Uniqueness, Inversion, and Stability Issues
  • Novel Tomographic Methods.
12:00-1:30 LUNCH
1:30-2:30 Rainer Kress,
"Inverse Obstacle Scattering: part 1"
  • Basics on the Helmholtz Equation;
  • the Direct Scattering Problem: Uniqueness,
  • Existence and Numerical Solution via Boundary Integral Equations;
  • the Inverse Scattering Problem:
    - Uniqueness,
    - Iterative Solution Methods,
    - Decomposition Methods,
    - Sampling and Probe Methods.
3:00-4:00 Rainer Kress,
"Inverse Obstacle Scattering: part 2"
Sunday 22 May
9:00-10:00 Coffee
10:00-11:00 Charles Groetsch,
"Inverse Problems and Regularization Theory; part 2"
11:00-12:00 Peter Kuchment,
"Tomographic methods in Imaging; part 2"
12:00-1:30 LUNCH
1:30-2:30 Jianhua Huang,
"Regularization Methods in Statistics"
  • A Classical Example: Ridge Regression
  • Function Estimation and Roughness Penalty
  • The Variable Selection Problem and Sparsity Inducing Penalty
  • Functional Data, One-way and Two-way
  • Sparse Principal Components and Bioclustering
2:30-3:30 Matti Lassas,
"Geometric methods for inverse problems"
  • Inverse conductivity problem with a matrix valued conductivity
    • how Riemannian metric and manifolds appear in inverse problems
    • counterexamples and invisibility cloaking
  • Inverse problems for the wave equation
    • Equivalence of the inverse problems in time domain for the wave equation, the heat equation, and the Schrodinger equation.
    • Travel time coordinates
    • Basic steps of reconstruction: From the boundary data to the inner products of the solutions and the determination of the travel time metric.
3:30-4:00 Break
4:00-5:00 Matti Lassas,
"Geometric methods for inverse problems"
 

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