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• Geometric Inverse problems and applications
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# Personnel

Matti Lassas (prof.)

Postdoctoral Researchers

Roberta Bosi (Ph.D.)

Tapio Helin (D.Sc. Tech.)

(Ph.D.)

PhD Candidates

Hanne Kekkonen (M.Sc.)

Jussi Korpela (M.Sc. Tech.)

Teemu Saksala (M.Sc.)

Esa Niemi (M.Sc. Tech.)

## Former Group Members:

Paola Elefante (works currently in the industry - Relex)

Hanne Kekkonen (currently a postdoc researcher at Warwick University)

Matteo Santacesaria (currently a postdoc researcher at Politecnico di Milano)

Henrik Kettunen (works currently in the industry - TDK Nordic)

Katya Krupchyk (currently an assistant professor at University of California)

Miren Zubeldia (works currently in the industry)

# What do we do?

Inverse problems are a branch of exact mathematics, pure and applied, where the goal is to find unknown parameters or structures by indirect measurements. A typical inverse problem is the inverse conductivity problem, called in medical imaging the Electrical Impedance Tomography. Its practical setting is the following: Assume that you want to find the inner structure of your torso by doing resistivity measurements at your skin. In mathematical terms, this means the problem of finding of the unknown parameter functions of a partial differential equation from the knowledge of the boundary values of the solutions.

# Research projects

### Electrical Impedance Tomography

In electrical impedance tomography (EIT) an unknown physical body is probed with electric currents with the goal of revealing the inner structure of the body. (more)

### Inverse problems on manifolds

For instance medical ultrasound imaging  and geophysical prospecting, are examples of inverse problems that can be studied using geometry. (more)

### Invisibility cloaking and metamaterials

Invisibility cloaking means covering  an object with a special material so that the electromagnetic waves go around the object. To the observer, an object coated in such a way is invisible. Today, the required coating materials can be made for electromagnetic waves with a specified microwave or visible light frequency. (more)

# International collaborators

Maarten de HoopPurdue University, USA

Allan GreenleafUniversity of Rochester, USA

Hiroshi Isozaki, University of Tsukuba, Japan

Yaroslav Kurylev, University College London, UK

Gunther Uhlmann, University of Washington, USA

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