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Wednesday, April 4, 2018

Pasquale Porcelli Lecture Series  Special Lecture Series

Posted November 7, 2017
Last modified January 29, 2018

2:30 pm - 3:30 pm Dodson Auditorium

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 1: The Mathematics of Inpainting

(The talk is intended to be accessible to High School Students.) In this talk we will illustrate how mathematical techniques can be used in image processing. These play an important role in the creation of digital inpainting methods with a wide spectrum of applications, such as in the process of image restoration of ancient frescoes where missing parts of damaged images are filled in based on the information collected from neighboring areas.


Pasquale Porcelli Lecture Series  Special Lecture Series

Posted November 7, 2017
Last modified January 29, 2018

4:10 pm - 5:10 pm Dodson Auditorium

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 2: Variational Problems in Materials Science

(Intended to be accessible to Undergraduate Students.) Abstract: Quantum dots are man-made nanocrystals of semiconducting materials. Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many
applications that permeate our daily lives, such as the new Samsung QLED TV monitor that uses quantum dots to turn "light into perfect color"!

Quantum dots are obtained via the deposition of a crystalline overlayer (epitaxial film) on a crystalline substrate. When the thickness of the film reaches a critical value, the profile of the film becomes corrugated and islands (quantum dots) form. As the creation of quantum dots evolves with time, materials defects appear. Their modeling is of great interest in materials science since material properties, including rigidity and conductivity, can be strongly influenced by the presence of defects such as dislocations.

In this talk we will use methods from the calculus of variations and partial differential equations to model and mathematically analyze the onset of quantum dots, the regularity and evolution of their shapes, and the nucleation and motion of dislocations.

Thursday, April 5, 2018

Pasquale Porcelli Lecture Series  Special Lecture Series

Posted November 7, 2017
Last modified January 29, 2018

10:30 am - 11:30 am Digital Media Center Theater

Irene Fonseca, Carnegie Mellon University
Porcelli Lecture 3: Variational Problems in Imaging Science

(The talk is intended to be accessible to Graduate Students.) Abstract: The mathematical treatment of image processing is strongly hinged on variational methods, partial differential equations, and machine learning. The bilevel scheme combines the principles of machine learning to adapt the model to a given data, while variational methods provide model-based approaches which are mathematically rigorous, yield stable solutions and error estimates. The combination of both leads to the study of weighted Ambrosio-Tortorelli and Mumford-Shah variational models for image processing.