# Image Processing Techniques with Applications to Shape and Surface Reconstruction

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In the first part of this talk, I will give a brief introduction to image

processing and discuss some of the classical models and techniques. In the

second part of the talk, I will discuss a model from my current research

that can segment or dissoclude objects in images by using additional shape

information. I will then show how this model can be easily adapted to the

application of reconstructing surfaces from unorganized data points in

space known as point clouds. Finally, some ongoing and future work will be

discussed which also includes some exciting undergraduate research

projects.

# Workshop on Applying for Mathematics Undergraduate Research Programs

# Schrdinger operators with Sturmian potentials : An interdisciplinary history

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I will be discussing a problem I am working on involving the spectral properties of Schrdinger operators with Sturmian potentials. This problem originated with a Nobel Prize-winning observation by a chemist in 1984. After being studied by math physicists, it was reduced to the purely dynamical behavior of a polynomial map on a manifold. The word "interdisciplinary" in the title of this talk refers both to a mathematical problem arising in another discipline and to the collaboration within mathematics across different research areas.

# What do Linear Algebra and Analysis have to do with Quantum Mechanics?

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Linear Algebra and Analysis approach mathematical abstraction from two seemingly different perspectives. However, once we start talking about normed linear spaces or, more concretely, Hilbert spaces, these two subjects readily connected to each other and the new theory ultimately became the playground for physicists in the 1900s. In this talk, we present some background material on both linear algebra and elementary analysis, discuss their roles within the concept of a Hilbert Space, and why a Hilbert space is important to Quantum Mechanics.